Control in Distribution Networks with Demand Side ...To simplify better understand the used approach, the first results here present show only the shifting loads procedure for one

i

FILIPE ANDRÉ DE SOUSA FIGUEIRA BARATA

Licenciado

Control in Distribution Networks with Demand Side Management

Dissertação para obtenção do Grau de Doutor em Engenharia Electrotécnica e de Computadores

Orientador: Prof. Doutor Rui Alexandre Nunes Neves da Silva, Professor Auxiliar, Faculdade de Ciências e Tecnologias da Universidade Nova de Lisboa

Júri:

Presidente: Prof. Doutor Jorge Joaquim Pamies Teixeira

Arguente(s): Prof. Doutora Teresa Maria de Gouveia Torres Feio Mendonça

Prof. Doutor João Francisco Alves Martins

Vogais: Prof. Doutor José Manuel Prista do Valle Cardoso Igreja

Prof. Doutor Miguel José Simões Barão

Dezembro, 2015

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Control in Distribution Networks with Demand Side Management

Copyright © Filipe André Barata, Faculdade de Ciências e Tecnologia, Universidade Nova

de Lisboa.

The Faculdade de Ciências e Tecnologia and the Universidade Nova de Lisboa have the

perpetual right, without geographical limits, to archive and publish this dissertation either in

print or digital form, or any other medium that is still to be invented, and distribute it through

scientific repositories, admitting its copy and distribution for educational or research purposes,

as well as for non-commercial purposes, as long as the author and the editor are credited for

their work.

A Faculdade de Ciências e Tecnologia e a Universidade Nova de Lisboa têm o direito,

perpétuo e sem limites geográficos, de arquivar e publicar esta dissertação através de

exemplares impressos reproduzidos em papel ou de forma digital, ou por qualquer outro meio

conhecido ou que venha a ser inventado, e de a divulgar através de repositórios científicos e de

admitir a sua cópia e distribuição com objetivos educacionais ou de investigação, não

comerciais, desde que seja dado crédito ao autor e editor.

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Acknowledgements

I wish to express my gratitude to my Supervisor Professor Rui Neves-Silva for the opportunity

he gave me and for the confidence he deposited in me, accepting this project inspired by him. I

also like to thank his support and understanding in the most difficult periods of this journey, and

by all his collaboration and advices which guided me until this moment.

Similarly, I would like to reserve a special acknowledgment to Professor José Manuel Igreja, for

his priceless academic, professional, personal guidance and encouragement.

For this work I would like also to thank my CAT committee member Dr. João Martins, for is

time, interest, and helpful comments.

I wish to personally thank my colleagues and friends from ISEL: Carla Viveiros, José Ribeiro,

Luís Encarnação, Nuno Domingues, Nuno Guedes, Pedro Fonte, Ricardo Luís e Rita Pereira.

These are fantastic people that provide me priceless moments and with whom I have the

privilege to share a considerable part of my days since I have started my academic life.

Finally, and most importantly, I am thankful for the emotional support of my family. To Manuel

Abreu Rodrigues, a tremendous friend that recently passed away, all my gratitude for his

contagious joy that had provided me and my family unforgettable moments. His unexpected

passing left me emotionally wounded, but allowed me to rethink better about my life. He will be

sorely missed. To my Mother and Grandmother; two super women, an example of strength and

determination. Despite all the drawbacks life brought them, they rose up and continued.

To my wife Paula, to my son Salvador and to the newly arrived daughter Joana, my gratitude for

being there every day with a smile and for the comfort and encouragement words, and also to

them, my apologies for all the absences required by this work.

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Abstract

The way in which electricity networks operate is going through a period of significant change.

Renewable generation technologies are having a growing presence and increasing penetrations

of generation that are being connected at distribution level. Unfortunately, a renewable energy

source is most of the time intermittent and needs to be forecasted.

Current trends in Smart grids foresee the accommodation of a variety of distributed generation

sources including intermittent renewable sources. It is also expected that smart grids will

include demand management resources, widespread communications and control technologies

required to use demand response are needed to help the maintenance in supply-demand balance

in electricity systems. Consequently, smart household appliances with controllable loads will be

likely a common presence in our homes. Thus, new control techniques are requested to manage

the loads and achieve all the potential energy present in intermittent energy sources.

This thesis is focused on the development of a demand side management control method in a

distributed network, aiming the creation of greater flexibility in demand and better ease the

integration of renewable technologies. In particular, this work presents a novel multi-agent

model-based predictive control method to manage distributed energy systems from the demand

side, in presence of limited energy sources with fluctuating output and with energy storage in

house-hold or car batteries. Specifically, here is presented a solution for thermal comfort which

manages a limited shared energy resource via a demand side management perspective, using an

integrated approach which also involves a power price auction and an appliance loads allocation

scheme.

The control is applied individually to a set of Thermal Control Areas, demand units, where the

objective is to minimize the energy usage and not exceed the limited and shared energy

resource, while simultaneously indoor temperatures are maintained within a comfort frame.

Thermal Control Areas are overall thermodynamically connected in the distributed environment

and also coupled by energy related constraints. The energy split is performed based on a fixed

sequential order established from a previous completed auction wherein the bids are made by

each Thermal Control Area, acting as demand side management agents, based on the daily

energy price. The developed solutions are explained with algorithms and are applied to different

scenarios, being the results explanatory of the benefits of the proposed approaches.

Keywords: DMPC, MAS, intermittent energy resource, DSM, energy auction, thermal control

areas, shifting loads, energy efficiency;

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Resumo

A forma como as redes elétricas operam está a atravessar um período de transformação

significativa. As tecnologias de geração renováveis possuem uma presença crescente e a

penetração desta geração ao nível da distribuição está a aumentar. Infelizmente, uma fonte de

energia renovável é na maioria do tempo intermitente e necessita de algum tipo de previsão e

antecipação de comportamento.

As têndencia actuais redes elétricas inteligentes preveêm que estas irão acomodar de uma forma

integrada, formas de armazenamento de energia e uma variedade de fontes de geração

distribuídas incluindo fontes renováveis intermitentes. É também expectável que as redes

inteligentes irão incluir sistemas de gestão da procura e a difusão da comunicações e tecnologias

de controlo necessários para que a resposta à procura auxilie no equilíbrio entre oferta e

demanda em sistemas de energia elétrica. Eletrodomésticos inteligentes serão provavelmente

uma presença comum nos nossos lares.

Desta forma, são necessárias novas técnicas de controlo para gerir as cargas por forma a

aproveitar todo o potencial energético existente em fontes de energia intermitentes.

Esta tese foca uma metodologia de controlo para gestão da procura em redes distribuídas, para

criar maior flexibilidade do lado da procura e facilitar a integração de tecnologias renováveis.

Em particular, o trabalho apresenta um novo método de controlo predictivo multi-agente para

gestão sistemas de redes de energia distribuídas do lado da procura, quando na presença de

recursos energéticos limitados e flutuantes, e com armazenamento de energia em baterias

domésticas ou de veículos. Especificamente, é aqui apresentada uma solução para conforto

térmico que gere um recurso energético limitado e partilhado numa perspetiva de gestão da

procura, utilizando uma abordagem integrada que envolve um leilão de preço de energia e um

esquema de alocação de cargas domésticas.

O controlo é aplicado individualmente a um conjunto de Áreas de Controlo Térmico, unidades

de demanda (consumidores), onde o objetivo é minimizar a utilização de energia sem exceder o

recurso partilhado e limitado enquanto, simultaneamente, a temperatura interior é mantida

dentro da zona de conforto. Em ambiente distribuído, as Áreas de Controlo Térmico estão

geralmente termodinamicamente ligadas e também acopladas pela restrição energética. A

distribuição da energia é efetuada com base numa ordem sequencial fixa estabelecida por um

leilão onde cada uma das Áreas de Controlo Térmico, atuando como agentes de gestão da

procura, faz as suas licitações com base no preço diário da energia. A solução desenvolvida é

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explicada por algoritmos e aplicada a diferentes cenários onde os resultados obtidos ilustram os

benefícios da abordagem proposta.

Palavras chave: Controlo Predictivo Distribuído, Sistemas Multi-Agente, recurso de energia

intermitente, gestão da procura, leilão de energia, áreas de controlo térmico, alocação de cargas,

eficiência energética;

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Table of Contents

Acknowledgements ............................................................................................. iii

Abstract ................................................................................................................ v

Resumo ............................................................................................................... vii

Table of Contents ............................................................................................... ix

List of Figures ................................................................................................... xiii

List of Tables ..................................................................................................... xix

List of Acronyms and Abbreviations ............................................................. xxi

1 Introduction .................................................................................................. 1

1.1 Introduction .................................................................................................................. 1

1.2 Background .................................................................................................................. 2

1.3 Motivation .................................................................................................................... 3

1.4 Research Questions ...................................................................................................... 5

1.5 Aimed Contributions.................................................................................................... 5

1.6 Outline ......................................................................................................................... 7

2 Literature Review and Model Based Predictive Control ....................... 11

2.1 Introduction ................................................................................................................ 11

2.2 Demand Side Management for Distribution Networks.............................................. 13

2.3 Model Based Predictive Control ................................................................................ 18

2.3.1 Linear Plant Model .......................................................................................................... 22

2.3.2 Nonlinear Plant Model .................................................................................................... 28

2.3.3 Generalized Predictive Control ....................................................................................... 29

2.3.4 Stability and Feasibility ................................................................................................... 33

2.3.5 Centralized MPC ............................................................................................................. 35

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2.3.6 Decentralized MPC ......................................................................................................... 37

2.3.7 Distributed Model Predictive Control ............................................................................. 39

2.4 Multi-Agents systems (MAS) .................................................................................... 44

2.4.1 MAS architectures ........................................................................................................... 45

3 Dynamical Models and Scenarios Description ........................................ 51

3.1 Introduction ................................................................................................................ 51

3.2 Scenarios overview .................................................................................................... 52

3.3 Demand side management approach ......................................................................... 56

3.4 TCA Dynamical Models ............................................................................................ 57

4 MPC and PI control in thermal comfort systems ................................... 65

4.1 Introduction ................................................................................................................ 65

4.2 System description ..................................................................................................... 66

4.3 Results ........................................................................................................................ 74

4.3.1 PI versus MPC. ................................................................................................................ 76

4.3.2 MPC with “comfort zone” ............................................................................................... 77

4.3.3 MPC with “comfort zone” and constrained available power .......................................... 79

4.3.4 Conclusions ..................................................................................................................... 80

5 Thermal Comfort with Demand Side Management Using

Distributed MPC ............................................................................................... 81

5.1 Introduction ................................................................................................................ 81

5.2 Implemented global scenario ..................................................................................... 82

5.3 MPC formalization .................................................................................................... 84

5.3.1 Algorithm I - Implemented sequential scheme ................................................................ 90

6 DMPC for Thermal House Comfort with Sequential Access

Auction ............................................................................................................... 91

6.1 Introduction ................................................................................................................ 91

6.2 Access order with fixed stablished sequence ............................................................. 92

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6.2.1 Results ............................................................................................................................. 93

6.3 Access order with variable hourly sequence ............................................................ 110

6.3.1 Algorithm II - Implemented sequential scheme with variable hourly sequence ........... 111

6.3.2 Results ........................................................................................................................... 112

6.4 Conclusions .............................................................................................................. 119

7 DMPC for Thermal House Comfort with Sliding Load ....................... 121

7.1 Introduction .............................................................................................................. 121

7.2 Algorithm III – Implemented shifting and loads allocation scheme ........................ 123

7.3 Results ...................................................................................................................... 126

7.3.1 One house scenario ........................................................................................................ 127

7.3.2 Distributed scenario ....................................................................................................... 131

7.4 Conclusions .............................................................................................................. 139

8 Conclusions and Future Work Directions ............................................. 141

8.1 Conclusion and Summary of Achievements ............................................................ 141

8.2 Recommendations for Future Work Directions ....................................................... 143

Bibliography .................................................................................................... 145

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List of Figures

Figure 2.1. Smart Grid Roadmap (Bsria, 2014) .......................................................................... 12

Figure 2.2. Venn diagram with implemented technologies. ........................................................ 12

Figure 2.3. Basic block diagram of MPC .................................................................................... 20

Figure 2.4. Conceptual picture of the moving horizon in predictive control (Boom &

Stoorvogel, 2010). .............................................................................................................. 21

Figure 2.5. Hard constraint representation (Adapted from Froisy, 1994). .................................. 25

Figure 2.6. Soft constraint representation (Adapted from Froisy, 1994). .................................... 25

Figure 2.7. GPC control structure. .............................................................................................. 31

Figure 2.8. Disturbance load profile in the several prediction horizons. .................................... 34

Figure 2.9. Indoor temperature profile for the several prediction horizons. ............................... 34

Figure 2.10. Power profile for the several prediction horizons. .................................................. 34

Figure 2.11. Consumption profile for several prediction horizons. ............................................ 35

Figure 2.12. Centralized MPC architecture (Scattolini, 2009). ................................................... 36

Figure 2.13. Decentralized MPC architecture (Scattolini, 2009). ............................................... 38

Figure 2.14. Distributed MPC architecture (Scattolini, 2009). ................................................... 40

Figure 2.15. Single-agent control structure. (Adapted from Negenborn 2007). ......................... 46

Figure 2.16. Multi-agent single layer control structure. (Adapted from Negenborn 2007). ....... 47

Figure 2.17. Multi-layer control structure. (Adapted from Negenborn 2007). ........................... 47

Figure 3.1. Typical smart grid architecture. ................................................................................ 51

Figure 3.2. Typical energy distribution communication architecture for smart grids (Adapted

from Siemens, 2014). ......................................................................................................... 52

Figure 3.3. Implemented scheme. ............................................................................................... 53

Figure 3.4. Thermal Control Area (TCA) smart thermostat controller vision. ........................... 54

Figure 3.5. Thermal Control Area concept.................................................................................. 54

Figure 3.6. Example of a TCA conceptual framework. .............................................................. 55

Figure 3.7. Energy modelling and building design process example with EnergyPlus. ............. 58

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Figure 3.8. Schematic representation of thermal-electrical modular analogy for one division. .. 60

Figure 3.9. Generic schematic representation of thermal-electrical modular analogy for several

divisions (Barata et al., 2014b). .......................................................................................... 60

Figure 3.10. TCA divisions interaction simplified scheme; ........................................................ 62

Figure 3.11. Generalized house/TCA scheme example. ............................................................. 63

Figure 4.1. Block diagram of the implemented system. .............................................................. 67

Figure 4.2. MPC with constraints, system block diagram ........................................................... 72

Figure 4.3. Outdoor temperature. ................................................................................................ 75

Figure 4.4. Indoor temperature. ................................................................................................... 76

Figure 4.5. Power and energy consumption. ............................................................................... 77

Figure 4.6. Temperature error with and without (MPC). ............................................................ 77

Figure 4.7. Case 1 - Indoor temperature with “comfort zone”. ................................................... 78

Figure 4.8. Case 2 - Indoor temperature with “comfort zone”. ................................................... 78

Figure 4.9. Power and energy consumption with “comfort zone”. ............................................. 79

Figure 4.10. Indoor temperature evolution with limited power. ................................................. 79

Figure 4.11. Power and energy consumption with limited power. .............................................. 80

Figure 5.1. Implemented sequential architecture scheme. .......................................................... 83

Figure 5.2. Daily consumer profile. ............................................................................................ 86

Figure 5.3. Thermally coupled TCA’s. ....................................................................................... 86

Figure 6.1: Heat transfer between divisions example. ................................................................ 92

Figure 6.2: System implementation scheme block diagram. ....................................................... 93

Figure 6.3. Outdoor temperature forecasting .............................................................................. 93

Figure 6.4. Scenario I - Disturbance forecasting and indoor temperature A1. ............................ 94



Figure 6.7. Scenario I - A1 power profile. ................................................................................... 95



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Figure 6.10. Scenario I - Global consumption characterization. ................................................. 97

Figure 6.11. Scenario I - Power profile. ...................................................................................... 97

Figure 6.12. Scenario I - Heating/cooling total cost. ................................................................... 97

Figure 6.13. Scenario II - Disturbance forecasting and indoor temperature A1. ......................... 98



Figure 6.16. Scenario II – A1 power profile. ............................................................................... 99

Figure 6.17. Scenario II – A2 power profile. ............................................................................... 99

Figure 6.18. Scenario II – A3 power profile. ............................................................................. 100

Figure 6.19. Scenario II - Global consumption characterization............................................... 100

Figure 6.20. Scenario II - Power profile. ................................................................................... 101

Figure 6.21. Scenario II - Heating/cooling total cost. ............................................................... 101

Figure 6.22. Scenario II - Batteries profile. ............................................................................... 101

Figure 6.23. Scenario III - Disturbance forecasting and indoor temperature A1. ...................... 102



Figure 6.26. Scenario III – A1 power profile. ............................................................................ 103



Figure 6.29. Scenario III - Global consumption characterization. ............................................ 104

Figure 6.30. Scenario III - Power profile. ................................................................................. 105

Figure 6.31. Scenario III - Heating/cooling total cost. .............................................................. 105

Figure 6.32. Scenario IV - Disturbance forecasting and indoor temperature A1. ...................... 106

Figure 6.33. Scenario IV - Disturbance forecasting and indoor temperature A2 ....................... 107

Figure 6.34. Scenario IV - Disturbance forecasting and indoor temperature A3 ....................... 107

Figure 6.35. Scenario IV – A1 power profile. ............................................................................ 107

Figure 6.36. Scenario IV - A2 power profile.............................................................................. 108

Figure 6.37. Scenario IV - A3 power profile.............................................................................. 108

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Figure 6.38. Scenario IV - Global consumption characterization. ............................................ 108

Figure 6.39. Scenario IV - Power profile. ................................................................................. 109

Figure 6.40. Scenario IV - Heating/cooling total cost. .............................................................. 109

Figure 6.41. Daily heating/cooling total cost. ........................................................................... 110

Figure 6.42. Outdoor temperature forecasting (Toa). ................................................................. 113

Figure 6.43. Fixed consumption profile 𝐶𝑤11, and priority level of TCA1. ............................ 113



Figure 6.46. Implemented system. ............................................................................................ 114

Figure 6.47. Access order. ......................................................................................................... 116

Figure 6.48. Disturbance forecasting and indoor temperature A1. ............................................ 116



Figure 6.51. Consumption and constraints to heat/cool A1. ...................................................... 117



Figure 6.54. Global consumption. ............................................................................................. 118

Figure 6.55. Heating/cooling total cost. .................................................................................... 119

Figure 7.1. Shifting load communication infrastructure. .......................................................... 122

Figure 7.2. Implemented shifting load scheme. ........................................................................ 122

Figure 7.3. Total consumption characterization. ....................................................................... 123

Figure 7.4. Implemented power distribution scheme starting in the Optimization Problem 1

(OPi) to OPNS. ................................................................................................................... 124

Figure 7.5.Outdoor temperature forecasting (Toa). .................................................................... 127

Figure 7.6. Thermal disturbance forecasting. ............................................................................ 127

Figure 7.7. Possible loads schedule combinations (PLSCs). ..................................................... 128

Figure 7.8. Total energy costs of FLSCS. .................................................................................. 129

Figure 7.9. Maximum available green energy and chosen sequence ........................................ 130

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Figure 7.10. Indoor temperature. ............................................................................................... 130

Figure 7.11. Used power to heat/cool the space and the maximum green resource available for

comfort. ............................................................................................................................ 131




Figure 7.15. Access order. ......................................................................................................... 133




Figure 7.19. Power profile A1. .................................................................................................. 135

Figure 7.20. Control input profile A1 ........................................................................................ 136


Figure 7.22. Control input profile A2. ....................................................................................... 137


Figure 7.24. Control input profile A3. ....................................................................................... 138

Figure 7.25. Batteries profile..................................................................................................... 138

Figure 7.26. Consumption costs. ............................................................................................... 138

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xix

List of Tables

Table 2.1. Simulation parameters for the several prediction horizons ........................................ 33

Table 2.2. Computational efforts under several prediction horizons .......................................... 35

Table 4.1.Simulation parameters for PIvsMPC ........................................................................... 76

Table 4.2. Simplified algorithm for MPC with “comfort zone”.................................................. 78

Table 6.1. Distributed parameters ............................................................................................... 94

Table 6.2. Scenario I - Penalty values ......................................................................................... 94

Table 6.3. Scenario III - Penalty values .................................................................................... 102

Table 6.4. Scenario III - Cost comparisons ............................................................................... 105

Table 6.5. Scenario IV - Penalty values .................................................................................... 106

Table 6.6. Example of hourly access order sequence to green energy ...................................... 111

Table 6.7. Bid value for each consumption level by agent. ...................................................... 114

Table 6.8. Scenario parameters. ................................................................................................ 115

Table 7.1.Scenario parameters .................................................................................................. 127

Table 7.2. Shifted loads characteristics ..................................................................................... 128

Table 7.3. Feasible Loads Sequence Combinations .................................................................. 129

Table 7.4. Distributed scenario parameters ............................................................................... 131

Table 7.5. Bid value for each consumption level by TCA ........................................................ 132

Table 7.6. Shifted loads characteristics for distributed scenario ............................................... 132

Table 8.1. Developed algorithm characteristics ........................................................................ 143

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List of Acronyms and Abbreviations

AMI Advanced Metering Infrastructure

ARMAX Autoregressive–Moving-Average Model with exogenous

inputs model

CPP Critical Peak Pricing

DER Distributed Energy Resources

DG Distributed Generation

DMS Distribution Management System

DR Demand Response

DMPC Distributed Model Predictive Control

DSM Demand Side Management

EMS Energy Management System

FLSC Feasible Loads Schedule Combinations

GPC Generalized Predictive Control

HVAC Heating Ventilation and Air Conditioning

I&C Interruptible and Curtailable Load

IL Interruptible Load

LQPC Linear-Quadratic predictive control

LTI Linear Time Invariant

MAS Multi Agent System

MBPC Model Based Predictive Control

MIMO Multiple-Input Multiple-Output

MO Market operator

MPC Model Predictive Control

MUSMAR Multistep Multivariable Adaptive Regulator

OCGT Open Cycle Gas Turbine

PEV Plug-in Electric Vehicle

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PLC Power Line Communication

PLSC Possible Loads Schedule Combinations

PTR Peak Time Rebate

RES Renewable Energy Sources

RHC Receding Horizon Control

RTP Real Time Pricing

SGPC Stable Generalised Predictive Control

SISO Single-Input Single-Output

TCA Thermal Control Area

TCL Thermostatically Controlled Loads

TOU Time Of Use

ZOH Zero-Order Hold

1

Chapter 1

1 Introduction

1.1 Introduction

Traditional electric power systems consist of large power generating plants, interconnected via a

high-voltage transmission lines, loading serving entities which deliver power to end users at

lower voltages using local distribution networks.

Importance of distributed generators (DGs) has increased significantly over the past few years

due to its potential for increasing reliability and lowering the cost of power through the use of

on-site generation. Development of small modular generation technologies, such as

photovoltaic, wind turbines and fuel cells has also contributed to this trend. However, novel

operational and control concepts are needed to make a proper integration into the power grid

system. Control strategies must be further developed to achieve the targeted benefits while

avoiding negative effects on system reliability and safety. The current power distribution system

was not designed to support distribution generation and storage devices at the distribution level;

compatibility, reliability, power quality, system protection and many other issues must also be

considered before the benefits of DGs can be fully obtained (Al-Hinai & Feliachi 2009).

A new emerging type of grid will soon be a reality. Smart Grids (SGs) are planned to include

decentralized generation, active network management for generation and storage, where the

actions of all connected agents to the electricity system can be intelligently integrated aiming for

a sustainable, efficient and secure energy supply system. Future SGs are anticipated to support a

variety of DG, including intermittent renewable sources (James & Jones, 2010).

Smart Grid concept is built on many of the technologies already used by electric utilities but

adds additional communication and control capabilities optimizing the operation of the entire

INTRODUCTION

2

electrical grid. Smart Grid is also positioned to take advantage of new technologies, such as

hybrid plug-in electric vehicles (PEV), various forms of distributed generation, solar energy,

smart metering, lighting management systems, distribution automation and many more.

In a scenario with strong presence of intermittent renewable energy sources (RES) that supply a

set of houses, the new techniques must developed to deal with smart devices, energy

management systems (EMS) such as programmable controllable thermostats and/or PEV

charge, and be capable of making intelligent decisions based on smart prices and users comfort.

Therefore, it is crucial to take into account a global solution that is able to take advantage of

these features.

1.2 Background

Since the beginning of electricity grids, demand has fluctuated and supply has been provided to

follow along. The intermittency of RES, such as wind or solar generation, stills nowadays the

major challenge for the integration of these resources. The present trend in power systems is to

connect more and more RES increasing significantly the security and the quality of supply.

One of the most common solutions to mitigate the problem is operating energy sources, such as

gas turbines or hydro power plants, balancing the variations. But, when the variations are

significant and change rapidly, the backup source needs to be higher and faster, leading to

increased carbon emissions. Also, widely used the frequency regulation is the direct measure of

the balance between generation and system demand at any one instant, and must be maintained

continuously within narrow statutory limits.

Another solution is the energy storage (Ribeiro et al. 2001; Koeppel & Korpas, 2006), if there is

a surplus in energy produced it is fed into the storage. Energy storage is especially critical when

managing the output of intermittent renewable resources, ensuring their generation capacity is

available when needed most, maximising their value, but presently technology available does

only provide answers in low generation time intervals. For example, depending on the size of

the battery pack, electric cars may store enough electricity to power a house for a few hours, and

with small modifications, car batteries can deliver stored power to a home and to the power grid.

As showed there are several solutions to overcome the issue of intermittency but all have

problems to be overcome. The desirable approach is that the demand should follow the source,

passing the control to the demand side, having demand side management (DSM) (Callaway,

2009; Hamidi, 2007). Due its benefits to consumers, enterprises, utilities and society, in the last

decades, many efforts have been made to having demand play a more active role in balancing

the system. DSM benefits are related with customer energy bills and peak power prices

INTRODUCTION

3

decrease, reduction in the need for new power plants, transmission and distribution, reduction in

air pollution and with a significantly increased in energy efficiency. With the growing interest in

intermittent RES use, new opportunities and challenges are triggering and obliging these efforts

to come true. Because of technology barriers and lack of automation, the traditional way of

implementing DSM is via price incentives, i.e. by lowering tariffs at times when the aggregated

demand is expected to be below average, so as to encourage the end user to shift flexible loads

towards these periods (Saffre, 2010). But, with the new technologic advances and world trends

around the SGs concept (Chebbo, 2007; Commission, 2006), and requiring this kind of grid

intelligent control and management based on advanced communication, monitoring solutions,

automation and metering, novel opportunities and challenges to DSM are emerging.

In the smart world, simple household appliances like dishwashers, clothes dryers, simple

electric heaters or heating ventilation or air conditioning (HVAC) systems are planned to be

fully controllable to achieve the network maximum efficiency. Renewable energy sources are

expected to be a common presence and all kWh provided by these technologies should be

efficiently applied. Active demand side management provide solutions to control the loads,

adapting them to the current RES.

Being an actual theme, and despite the present trends and R&D efforts, SGs are still in the

“implementation phase”. More research is needed to provide solid solutions to overcome all the

constraints and turn into reality this ambitious vision. Smart Grids involve a mix of concepts:

distributed generation, DSM, intelligent control, energy efficiency, intermittent RES, thermal

comfort, load control and energy saving are some of them which are interconnected and should

be integrated into solutions. Smart Grids are, therefore, the most efficient approach to integrate

DG and RES in a coordinated way with demand management in a sustainable system (Blanquet

et al., 2009). To take advantage from the innovative technology characteristics provided by

future smart grid, it is necessary the development of new models and control techniques which

can support and manage all the mentioned concepts and, at the same time, deal with the network

complexity and its distributed nature (Werbos, 2011).

1.3 Motivation

Currently buildings account for 40% of the world’s energy consumption and almost half of the

today’s greenhouse gas emissions. This means buildings contribute to more greenhouse gases

emissions than traffic; which is estimated at 31%. Industry is estimated at 28%. When we

breakdown and analyse building’s energy consumptions, the most worrying aspect is that most

of this energy is used for heating or cooling (StorePET, 2014).

INTRODUCTION

4

In Europe, the energy use in buildings has overall seen a rising trend over the past 20 years. For

example, in 2009, households were responsible for 68% of the total final energy use in

buildings, mainly due to space heating responsible for around 70% (Nolte, 2011). This

increasing energy consumption is mainly to fulfil the demand for thermal comfort, being

presently the HVAC systems the principal energy end use in buildings (Korolija et al., 2011).

By these facts, it is socially, environmentally and economically imperative to decrease the

energy consumption by increasing the buildings efficiency. A viable choice to achieve the

reduction of energy consumption in the building sector is the application of demand response

(DR) mechanisms. Demand Response program, is an efficient load management strategy for

customer side, it is nowadays mostly used with the encouragement of customers to shift their

habits wisely according to electricity price variation during daytime (Siano et al., 2014). The

DR potential it is not sufficiently explored, being the two key challenges to work with diverse

heterogeneous loads and with the distributed nature of renewable sources. New technology

advances in communication are providing solutions to overcome the current electricity demand

requirements. This new development has accelerated devising various industrial programs for

scheduling utilization of residential appliances (Wang et al., 2015). This DR mechanisms

combined with DSM methodologies will be relevant in the future distributed SGs (Mahmood et

al., 2014), and provide solutions that allow buildings to be fully integrated and prepared to

efficiently coexist in an dynamic and inconstant environment typically supported by renewable

resources (Figueiredo et al, 2010). Nowadays the production of electricity system follows the

load. However, the renewable sources of electricity are essentially intermittent and it is vital to

provide flexibility to the grid to absorb the variations from these sources. In the intelligent

energy system (Smart Grid) the production controls the consumption. For example, when the

wind blows or the sun shines, buildings consumption must be automatically adjusted and

consumers will go from being passive participants to be active players in the electricity system.

Several solutions are emerging to deal with the variability, flexibility and poor controllability of

the green sources and consequently on the ability to maintain the balance between demand and

supply. Remark that, DSM strategies must have into account the control of many kinds of

appliances, for instance, HVAC systems, lighting or electric vehicles charging.

The methodology here presented seeks a solution to respond to this variability, implementing,

with the technological and advanced environment that SGs are projected to provide (Paul et al.,

2014), pursuing new technologies and solutions that will allow simple home appliances to be

entirely controllable. Also, this active DSM is able manage the loads to obtain harmony in

demand supply ratio.

INTRODUCTION

5

1.4 Research Questions

With SGs, domestic customers will pass from static consumers into active participants in the

production process. Final user’s participation can be achieved due to the development of new

domestic appliances with controllable load. Shifting their electricity consumption in time or, by

changing their work conditions, these devices can be controllable, adjusting the demand to the

desired intermittent source without decreased the comfort of the residents. In distributed

networks, aggregated to an intermittent source, an unlimited number of this kind of loads can

exist, representing a control problem to achieve the network efficiencies, involving

stakeholder’s satisfaction. To incorporate this in system design and analysis, demand response

needs to be supported by scientific methodology based on analysis and models verifiable by

experiment. How to improve energy efficiency using this domestic potential is still not well

studied and needs to be a research topic.

Considering the mentioned above, this work aims providing solutions to answer the following

research questions:

Q.1 How, in a distributed network, can the demand be adjusted to an intermittent source to

maximize the energy efficiency?

Q.2 How to improve energy efficiency using the domestic potential in a distributed network?

Q.3 Which control methods should be applied in a distributed network with demand side

management to obtain all the existing energy potential from intermittent energy sources?

The adopted work hypothesis to address the research question is defined below:

Using an integrated approach, that in a distributed environment, considers multi-agent

control scheme and an optimization MPC multi-objective approach with anticipative effect,

capable to deal in a DSM perspective, with fluctuating energy sources, smart load control,

thermal comfort and real-time price negotiation.

1.5 Aimed Contributions

The work here presented is distinct and has the advantage of providing a solution that integrates

set features and concepts that are also the smart grid bases, such as intelligent control,

distributed generation, energy efficiency, energy saving, DSM, fluctuating energy sources,

smart load control, thermal comfort, real-time price negotiation and energy auction markets

mechanisms. These characteristics deliver a unique structure where the grid connected entities

actions can be intelligently combined, aiming for a more efficient, secure and sustainable energy

system. So, the work intends to provide an innovative solution involving an integrated

INTRODUCTION

6

Distributed Model Predictive Control (DMPC) to manage networks that is able to efficiently

adapt the consumption to an intermittent renewable source. It provides news developments in

DSM with renewable energy sources and backup fossil energy using an hourly auction

mechanism access and a load allocation scheme that allows managing the loads in order to

balance demand and supply. The proposed sequential multi-agent DMPC scheme for thermal

house comfort and energy savings provides robustness, adjustment and flexibility to the global

system. Also the work presents an energy usage optimization scheme with DSM in which the

consumer as the flexibility to choose by the hour between comfort or energy savings.

The proposed integrated solution provides several scientific contributions that have been

developed under the framework of this thesis:

C.1 New developments in DSM, for different thermal areas, exploit an integrated

optimization approach able to cope with intermittent renewable energy sources

and backup fossil energy using an hourly auction mechanism access - the obtained

solution allows managing the loads in order to balance demand and supply. The DSM

optimization process uses a routine that finds a constrained minimum of a quadratic cost

function that penalizes the sum of several objectives, which based on energy forecasts

and several other inputs, is able to adjust the energy consumption to an intermittent

renewable resource or even restrict it to this type of resource in detriment of fossil

sources. An auction mechanism allows stablishing an access order to the renewable

source based on an hourly energy bid. Sequentially, the controllers transmit between

them the information about the available energy;

C.2 TCA dynamic model with multi-zone dynamically coupled areas is developed -

the developed model is built for infrastructures composed by several adjacent areas that

may thermally interact among them. The dynamical model allows each room to be

treated independently, with its own construction features, thermal disturbances, comfort

requirements, energy costs and consumption needs. When distinct divisions thermally

interact the information about the predicted indoor temperature is transmitted between

them. This change of information allows to each controller a greater understanding

about the surrounding environment and consequently improving the decision-making

ability;

C.3 A novel sequential scheme for DSM based on multi-agent DMPC for thermal

house comfort and energy savings is reported - the proposed sequential scheme

provides robustness, adjustment and flexibility to the global system. The sequence is

built based on an energy bid where the highest biddings are placed first in the access

order. After consume, each agent predicts its consumption profile and pass throw the

next, the information about the predicted available renewable energy. At each hour, the

INTRODUCTION

7

sequence is established and the energy price depends from the offered bid, amount and

type (renewable or grid) of energy consumed;

C.4 Shifting load algorithm for loads allocation - customer sets features of flexible

loads and the algorithm fits them in the most favourable time interval gap. Each

customer select for each division, the characteristics of the loads, the load value, its

duration, the turned on time and the “sliding level” of the “shifted loads”. With this

information the algorithm finds all the possible load combinations and from these

selects only the feasible ones. The feasibility of the loads is related to the predicted

hourly available power, so, at each instant the look forward and tries fitting the loads in

gaps that privileges the consumption of renewable energy. Thus, in a distributed

environment with energy and comfort constraints, the algorithm is able to find the best

hour to turn on the loads;

C.5 Energy usage optimization scheme with DSM adjustable parameters - with the

developed optimization scheme the consumer has the flexibility to choose hourly

between comfort or energy savings. Each controller provides to the consumer a set of

parameterizations which according to his consumption perspective, space occupancy

schedule, indoor temperature preferences and energy cost, provides to the user the

ability to be hourly in his most convenient state.

1.6 Outline

This dissertation is structured as follows:

Chapter 1 – Introduction, here is performing a brief introduction with a background analysis,

followed by the research problem. The chapter also states the main original contributions of the

work and in the end the outline of the thesis is presented.

Chapter 2 – Literature Review and Model Based Predictive Control, the focus of this chapter

is to perform a background analysis on the main topics of the thesis, Demand Side Management,

Multi-Agent-Systems and Model Based Predictive Control. The chapter also includes general

review on distributed model predictive control formalization for complex large-scale dynamical

systems.

Chapter 3 – Dynamic Models and Scenarios Description, the main ideas and models that

support the research developed are presented. The chapter starts by presenting the general

abstract problem, the conceptual scenarios and describe the system architecture. Finally, the

developed dynamic model is addressed using a line state-space model approach.

INTRODUCTION

8

The elaboration of this chapter provided relevant matter that was originally included in part in

the following publications (Barata et al., 2014a; Barata et al., 2014b).

Chapter 4 – MPC and PI control in thermal comfort systems chapter presents the fundamental

approach towards the final developed structure. Is the first seed which allowed us to understand

the problem, its dynamics and to verify that the MPC control strategy is suitable for the

objective that is intended to be achieved. The methodologies are based on a predictive control

structure associated to a PI controller and applied to the thermal house comfort in an

environment with limited energy sources. The predictive control is compared with the

traditional control methods used in thermal systems. Also, it was created a temperature “comfort

zone” to weight only the temperatures outside the gap, instead of traditional system were all

deviations are weight. Simulation results and analysis also complement two distinct situations

where the system reacts differently if the indoor temperature is inside or outside the “comfort

zone”.


the following publications (Barata et al., 2012a).

Chapter 5 – Thermal Comfort with Demand Side Management Using Distributed MPC, this

chapter presents a DMPC methodology for indoor thermal comfort which simultaneously

optimizes the consumption of a limited shared energy resource. Firstly, the global scenario and

all the made assumptions that support the thesis are described. Also, the implemented sequential

architecture scheme is pictured. Secondly, the control objective is defined and the tailored

DMPC optimization problem is detailed, formalized and exemplified.

The Algorithm I which describe implemented sequential scheme is presented. This algorithm

represents the basic structure for more complex schemes.

Chapter 6 – DMPC for Thermal House Comfort with Sequential Access Auction, this chapter

presents the obtained results achieved with the developed integrative methodology to manage

energy networks from the demand side with strong presence of intermittent energy sources and

with energy storage in house-hold or car batteries.

The results are pictured with and without batteries support and two different approaches are

considered, the energy split based on a fixed sequential order, and with the energy split varying

hourly based on a bid value directly related with the consumption profile behaviour. The

Algorithm II, which describes implemented sequential scheme with variable hourly sequence

and energy storage, is also presented.


the following publications (Barata et al., 2012b; Barata et al., 2013a).

INTRODUCTION

9

Chapter 7 – DMPC for Thermal House Comfort with Sliding Load chapter presents the

developed DMPC integrative solution which is able to, in a distributed network with multiple

TCAs, adjust the demand to an intermittent limited energy source, using load shift and

maintaining the indoor comfort. The Algorithm III which describes the implemented shifting

and loads allocation scheme is presented followed by the results and its analysis. The

elaboration of this chapter provided relevant information that was included in the following

publications (Barata et al., 2013c) and more detailed in (Barata et al., 2014c).

Chapter 8 – Conclusions and Future Work Directions, in this last chapter, discusses the main

conclusions of this work, detailing the problems found along the way and pointing out potential

solutions for them. Additionally, the main results and contributions are summarised, and some

possible directions for further research are mentioned.

INTRODUCTION

10

11

Chapter 2

2 Literature Review and Model Based

Predictive Control

2.1 Introduction

Future SGs are expected to include distributed generation, demand side management, intelligent

control, energy efficiency, intermittent RES, thermal comfort, load control, real-time price

negotiation and energy saving (IEA, 2011). These concepts are the smart grid bases, where the

actions of all agents connected to the electricity system can be intelligently integrated aiming for

a sustainable, efficient and secure energy supply system.

Being an actual theme, and despite the present trends and R&D efforts, SGs are now giving the

firsts steps in the implementation phase, Figure 2.1, with small projects and grid prototypes all

over the world (EcoGrid, 2014; DOE, 2014). More research is needed to offer solid solutions to

overcome all the constraints and turn real this ambitious vision.

In a scenario with strong presence of intermittent RES that supply a set of houses, it is possible

to manage several loads in each house in order to: 1) adjust the demand to the supply; 2)

maintain indoor thermal comfort; 3) achieve lower energy costs 4) reduce CO2 emissions. Using

a demand side management approach, the distributed loads can be manage by negotiating in real

time the energy price and the consumer comfort in order to guarantee the balance between

demand and the intermittent source. The main goal is to develop new control methods and

methodologies to manage future SGs with demand side management with high penetration of

intermittent resources.

LITERATURE REVIEW

12

Figure 2.1. Smart Grid Roadmap (Bsria, 2014)

The method uses the match results between demand and supply to decide the control actions to

be implemented on the demand side. It is considered environmental and pre-establish variables

as a decision-making factor. By using this active DSM control, the optimal control strategies for

various appliances can be generated whilst maximum utilisation of energy supplied from

intermittent systems is guaranteed. In a distributed network, with several loads at different

locations control actions applied for solving a local energy problem can create lack of energy at

a different location in the network. Therefore, coordination control strategies are required to

make sure that all available control actions serve the same objective. To support the idea, it is

consider multi-agent control schemes in which each agent will employ a model-based predictive

control approach. The agents communicate and negotiate in a distributed network environment,

to improve decision making, and, by adjusting the demand to the source, the maximum energy

potential existent in the intermittent source can be achieved.

Figure 2.2. Venn diagram with implemented technologies.

MBPC

DSMMAS

LITERATURE REVIEW

13

At the same time, as referred, is also desirable no or negligible impact on end users/occupiers.

Thus, this literature review intend to show what are the main research trends related with the

three main support ideas that interact in this work, DSM, Multi-Agent Systems (MAS) and

Model Based Predictive Control (MBPC), Figure 2.2.

2.2 Demand Side Management for Distribution Networks

To reach important reduction in CO2 emissions, the RES will be the main contributors to the

electricity generation systems. Presently, the solar and wind power, are the renewable energy

technologies that are commercially available with sufficient scalable. Although the expected

growth of these sources through to 2020 target is envisioned, there are real concerns about the

variability, flexibility and poor controllability of the sources and consequently on the ability to

maintain the balance between demand and supply. The growing uncertainty in power systems

coupled with the introduction of power markets calls for the development of new tools for

planning, operations and market-based decision-making. To deal with this uncertainty due to the

dissemination of renewables, the systems will need, for example, to apply bigger amounts of

reserve that is generally provided by a combination of synchronised and standing reserve.

Besides to synchronise reserve provided by part-loaded plant, the balancing task will also be

supported by standing reserve, which is supplied by a plant with higher fuel and environmental

costs, such as Open Cycle Gas Turbine (OCGT), or through more desirable techniques such as

storage facilities or DSM.

Demand Side Management was introduced in USA by Electric Power Research Institute (EPRI)

in the 1980s (Balijepalli et al., 2011) and has been traditionally seen as a means of reducing

peak electricity demand so that energy suppliers could diminish the construction of new

capacity. Therefore, to decrease peak load, DSM is mainly applied via price incentives, with the

existence of lowering tariffs at times when the aggregate demand is expected to be below

average to encourage the end user to shift flexible loads towards those periods. By reducing the

overall load on an electricity network, DSM provides numerous benefits: increasing system

reliability, reducing of the dependency on energy importation, reducing energy prices,

stimulates energy markets competitively, reducing harmful emissions to the environment and in

avoiding high investments in generation, transmission and distribution networks. Thus DSM

applied to electricity systems provides significant financial, reliability and ecological benefits.

With the power markets development, new emerging technologies and the new power grid

concepts (microgrid, smart grid), innovative solutions are giving more relevance to DSM

strategy. Generally, DSM programs are separate in these four categories:

LITERATURE REVIEW

14

Energy efficiency, the user decreases the demand for energy without sacrificing the

benefits received from energy (e.g. installing building insulation, purchasing more

efficient appliances);

Conservation, the consumer decreases his energy demand by reducing their energy

usage (e.g. adequate thermostat temperatures, turning off lights);

Load management, the energy demand is reduced during periods of peak demand

when capacity is limited and the cost of energy provision is high;

Public information, which encourages customer participation in energy efficiency,

conservation, and/or load management activities through public campaigns, direct to

customer communication, or increasing customer access to information about their

consumption of energy services.

DSM directly benefits utilities in the following ways:

Distribution - only utilities avoid having to purchase additional peaking and base-load

energy resources. From the volatile wholesale energy market;

Electricity generating utilities avoid the cost of securing fuel and pollution abatement

for peaking and base-load power plants, while deferring expensive investments in new

power plants and their associated compliance costs;

Both kinds of utilities avoid costly investments in new transmission and distribution

infrastructure.

Utilities may in turn pass these savings on to consumers, resulting in lower utility bills. In

addition, DSM directly benefits utility customers in the following ways:

Many DSM programs provide financial incentives (such as rebates, bill credits, lower

rates, or low interest financing) to encourage customers to make choices that reduce

their energy consumption overall or during periods of peak demand;

By encouraging customers to reduce their energy usage or to consume energy during

times when energy services are less costly, DSM programs help customers to reduce

their monthly utility bill.

Demand response is a class of DSM programs in which electricity companies offer incentives to

clients to reduce their demand for electricity during periods of critical system conditions or

periods of high market power costs. DR programs are normally classified according to the

customer motivation method and the criteria with which load reduction “events” are triggered or

initiated. So, when the utility offers customers payments for reduction of demand during

specified periods, the program is called load response. But, when customers voluntarily reduce

their demand in response to forward market prices, the program is called price response.

Customers reduce load during those periods when the cost to reduce load is less than the cost to

LITERATURE REVIEW

15

generate or buy the energy. In this context, brief descriptions of these DR techniques that are

presently worldwide being applied and studied are now described.

Load-Response Programs

In load-response programs, utilities offer customers payments for reducing their electricity

demand for specified periods of time.

Direct load control

Direct load control is applied to domestic appliances that can be switched on and off during

periods of time using remote appliance controllers. The most common applications are the ones

that account for the most significant portion of energy demand, HVAC systems and water

heaters;

Load limiters

Load limiters have the intent to limit the power that can be used by consumers. This approach

temporarily disconnects parts of the installation, most often the HVAC or electrical heating

during power peaks. This scheme can also provide some flexibility to users to decide which

appliances to use now and what can be delayed;

Interruptible and Curtailable Load (I&C)

Interruptible and Curtailable-load programs are relatively simple to implement, the customers

agree to decrease or turn off pre-established loads for a period of time when notified by the

utility. Clients can switch off loads or adjust settings. Utilities must notify customers before an

interruptible/curtailable load event. As reward, participants receive lower electricity bills during

normal operation, as well as additional incentives for each event;

Frequency regulation

System frequency is the direct measure of the balance between generation and system demand

at any one instant and must be maintained continuously within narrow statutory limits.

Recently, there have been initiatives to investigate a technology that can be incorporated into

electrical appliances to provide frequency regulation (Dynamic Demand, 2014);

Scheduled Load

Scheduled load reductions are pre-planned between the utility and customer. Clients receive bill

reductions, as well as significant advance notification, since contractual agreements are set

months ahead. The advantage of this program is that customers can plan to reduce load on pre-

determined days;

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16

Price-Response Programs

These programs allow customers to voluntarily reduce their demand in response to economic

signals.

Time of use pricing

Time of use (TOU) tariffs are designed to more closely reflect the production and investment

cost structure, where rates are higher during peak periods and lower during off-peak periods.

Basically, instead of a single flat tariff for energy use, TOU tariffs are plan to be higher when

electric demand is higher, meaning that when you use energy is as important as how much you

use. These programmes are commonly practiced in a large number of countries, particularly for

households with electric heating;

Dynamic/Real Time Pricing (RTP)

The dynamic imposed by the existing deregulated market is based on real time system of supply

and demand. Prices change time to time and hour to hour depending upon these two factors. By

exposing customers to RTP i.e. time-varying prices, they can have a better view of the

prevailing market and the information and incentive to reduce their demand at peak times or

critical peak prices (CPP) and by this way provide a financial incentive for participants to shift

optional activities, such as clothes washing and drying and dishwashing, to times other than

critical peak periods;

Demand bidding

Demand bidding programmes are available when the customer is willing to negotiate is

consumption needs in detriment of cost reductions. So, the client is disposed to decrease or

sacrifice his consumption of electricity at a certain predetermined price. For example, this

technology can be applied to a smart thermostat which controls the indoor comfort equipment’s.

So, depending from real time electricity price levels, the thermostat can be programed to allow

different sceneries in different schedules.

In buildings, novel solutions that integrate occupant behaviour within the building in relation to

energy consumption are emerging (Virote & Neves-Silva, 2012).

Only with smart metering and smart appliances technology the mentioned programs are viable.

With smart meters consumer can see exactly what power loads are driving up their energy use

and make specific changes, (Navetas, 2014). This information combined with time flexible

smart electrical appliances (HVAC systems, water heaters, refrigeration, lighting, etc.) can lead

to much better energy efficiency.

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17

As showed, DSM will have an important role in the future smart grids architecture (Chen et al.,

2010; Luo et al., 2010) and by this reason many studies are being performed involving the

mentioned DSM techniques to provide future implementation solutions.

Callaway (2009), with the goal of delivering services such as regulation and load following,

developed new methods to model and control the aggregated power demand from a population

of thermostatically controlled loads (TCLs). The researcher manipulates the temperature set

point in order to control the demand curve and adapt it to a wind plant power source. The work

showed that it is possible the demand to follow the source with small changes in the nominal

thermostat temperature set point. With similar objective, Jun (2009), developed an algorithm

capable of controlling loads based on the available supply at certain time. The objective of the

algorithm is to minimize the impact on users and at the same time maximize the match between

demand and supply through identifying the best combinations of different demand side control

options such as load shifting, load control (on/off control and proportional control) and load

recover for various demand loads.

A potential application for controllable domestic heat loads, and flexible distributed generation

in power systems with significant capacities of uncertain wind generation is described in

(Savage et al, 2008). Heat load is effectively controlled by remote adjustment of thermostat set

points. The system transmit a signal to reduce heating load set points when net demand is

greater than the forecast value and a reserve shortfall was imminent. Zaidi et al., (2010) follows

a DSM approach, where unessential loads get selectively disconnected from the grid in an

under-generation scenario. In order to automatically detect unessential loads, load recognition

on the basis of measured consumption data can be performed. With the same objective of peak

shaving and balance between demand and supply, (Molderink et al., 2010), shows that with the

use of good predictions, in advance planning and real-time control of domestic appliances,

better matching of demand and supply can be achieved. With a similar approach, several other

studies can be found (James & Jones, 2010; Krishnappa, 2008).

As presented, several methods are focus in the development of load control manipulation

models, however, DSM is also been studied via models that use electricity incentive prices to

promote load management (Yang et al., 2006; Hamidi et al., 2008; Aalami et al., 2008; Yu &

Yu 2006; Shaikh & Dharme, 2009).

The desire DSM methodology that is intended to be achieved is a mix of these two solutions. It

intends to take advantage from the innovative technology characteristics provided by future

smart grids. It is expected that every electric house appliance will be controllable and the

communication infrastructures will allow RTP arrangement. At the same time, is desirable to

maximize the efficiency of renewable energy resources and minimize the consumer energy

LITERATURE REVIEW

18

costs. New models and control techniques must be developed to be capable of not only to

manage loads based on the available supply at a certain time, but also by negotiating in real time

the energy price and the consumer comfort (without significantly compromising the user

satisfaction) in order to guarantee the balance between demand and the intermittent source.

In a scenario with strong presence of intermittent RES that supply a set of houses, the new

solution must include smart devices, energy management systems (EMS) such as programmable

controllable thermostats and/or PEV charge, capable of making intelligent decisions based on

smart prices and users comfort.

2.3 Model Based Predictive Control

The firsts predictive controllers concepts were born from optimal control methodologies, such

as the Linear Quadratic (LQ) or the Linear Quadratic Gaussian (LQG) controllers in the

early’70s (Anderson and Moore, 1971). Only in late 70's that the first two truly MPC control

laws arise, the Identification-command (IDCOM) and the Dynamic Matrix Control (DMC),

which are acknowledged as the roots of MPC. These two methods share some common features

which established the basis of MPC.

The predictive control based on model MBPC is nowadays as one of the most popular and

efficient control strategies in industry. So, during the last two decades a growing interest has

been granted to model predictive control (MPC) due to its ability to handle constraints in an

optimal control environment (Moros an et al., 2010; Mosca, 1995). It is expected that soon MPC

may substitute the majority of the classic controllers that are becoming inefficient in complex

environments.

MPC is a form of control in which the current control action is obtained by solving on-line, at

each sampling instant, a finite horizon open-loop optimal control problem, using the current

state of the plant as the initial state, the optimization yields an optimal control sequence and the

first control in this sequence is applied to the plant. The major advantages that have contributed

for the success of this method are (Orukpe 2005; Jimenez 2000):

It handles multivariable control problems naturally, Single-Input/Single-Output SISO)

and Multiple-input/Multiple-Output (MIMO) formulations are similar;

Difficult dynamics such as dead-times, unstable or non-minimum phase systems can be

easily handled;

Feedforward compensation of measurable disturbances can be introduced in a natural

way exploiting the model-based and predictive features of the MPC methodology by

using disturbance models;

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19

It can take account of actuator limitations The incorporation of constraints in the

manipulated and controlled variables and/or states is a simple task. Constraints can be

considered at the controller design stage and the resulting optimisation problem can

often be solved using standard Linear Programming (LP) or Quadratic Programming

(QP) tools. It also allows operation closer to constraints, hence increased profit;

MPC controllers have been developed either for linear or non-linear models;

Methods which guarantee the stability of the closed-loop system are available;

Robustness features can be enhanced through tuning parameters or optimisation

methods. Constraint handling is, indeed, one of the most appealing properties of MPC,

since limits of several kinds always occur in practice.

Constraints can be used to describe several security limits, physical restrictions, technological

requirements and so on. These requirements must be handled at the controller design stage to

avoid undesirable performance. Constraints have two main objectives. They can be used to

increase the accuracy of the model, incorporating on it the actuator and plant limits and also be

used as tuning knobs to describe control requirements or specifications. Typically, optimal

operating point lies close to (or on) one or several limits and therefore, representing an

advantage from an economical point of view when it operate as close to the constraint boundary

as possible. Constraints can be classified according to different criteria. The following

classification of constraints, according to practical considerations, is due to Álvarez and de

Prada (1997):

Physical constraints. These limits, which must never be surpassed, are determined by

the physical limitations of the system;

Operating constraints. These bounds are fixed by the plant operators to specify the

optimal operating region. The operation constraints are more restrictive than he physical

limits;

Optimization or set point conditioning constraints. These limits, more restrictive than

the operating constraints, are used only if the set point conditioning technique is

applied;

Working constraints. These are the actual constraints considered by the controller to

determine the feasible region. The working constraints are obtained by choosing the

most restrictive among the physical, the operating and the optimization limits. Apart

from constraint handling, the relevant issues of stability and robustness have been

successfully tackled in the last decade.

The MPC block diagram is present in Figure 2.3 where the main blocks represent:

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20

Reference Trajectory - represents the desire signal to future outputs. The previous knowledge

of this trajectory provides the anticipative effect of this controller;

Model - the mathematical model, linear or nonlinear, that represents the process must be

capable to describe its dynamic behavior with sufficient accuracy;

Predictor- trough the mathematical model provides the future outputs based on the actual plant

information;

Optimizer - minimizes the cost function at every time sample to obtain the control action that

guaranties the system performance. When linear models are used and the problem is

unconstraint, the quadratic cost function presents a analytical solution, otherwise, some numeric

optimization methods must be used.

As can be seen, the presence of the plant model is a necessary condition for the development of

the predictive control. The success of MPC depends on the degree of accuracy of the plant

model (Zheng 2010).

Figure 2.3. Basic block diagram of MPC

Predictive control uses the receding horizon principle. This means that after computation of the

optimal control sequence, only the first control sample will be implemented, subsequently the

horizon is shifted one sample and the optimization is restarted with new information of the

measurements. The prediction horizon remains the same length despite the repetition of the

optimization at future instants. Since the state prediction x and hence the optimal sequence u*

depend on the current state measurements 𝑥(𝑘), this procedure introduces feedback into the

MPC law, providing a degree of robustness to modelling errors and uncertainty. Figure 2.4

explains the idea of receding horizon.

OPTMIZER

MODEL

(ESTIMATOR)

PROCESS

PREDICTOR

control

Predicted

error

Predicted

output

output +

–

REFERENCE

TRAJECTORY

COST

FUNCTION CONSTRAINTS

u(k)

𝑦 (𝑘 + 1)

r(k)

y(k)

𝑥 (𝑘)

LITERATURE REVIEW

21

Figure 2.4. Conceptual picture of the moving horizon in predictive control (Boom &

Stoorvogel, 2010).

In Figure 2.4 Nm, NC and HP represents is the minimum cost horizon, the control horizon and

prediction horizon respectively. At time k the future control sequence {𝑢(𝑘|𝑘), . . . , 𝑢(𝑘 + 𝑁𝑐 −

1|𝑘)} is optimized such that the performance-index J(u, k) is minimized subject to constraints.

At time k the first element of the optimal sequence (𝑢(𝑘) = 𝑢(𝑘|𝑘)) is applied to the real

process. At the next time instant the horizon is shifted and a new optimization at time k+1 is

solved.

The goal of MPC is to minimize a cost function over a given prediction horizon period. This

cost function should give an indication for the performance of the system. The control signal

contains the setting for the control measures that are able to influence the system, and the

constraints may contain the upper and lower bounds on the control signal, but also linear or non-

linear equality and inequality constraints on the control inputs and the states of the system.

In MPC, control decisions, system inputs, u(k) are made at discrete time instants k = 0,1,2,...,

which usually represent equally spaced time intervals. At decision instant k, the controller

samples the state of the system x(k) and then solves an linear optimization problem of the

following form to find the control action:

𝑚𝑖𝑛𝑢 𝐽(𝑥, 𝑢; 𝑥(𝑘)),

(2.1)

𝑠. 𝑡. 𝑥(𝑘 + 1) = 𝐴𝑥(𝑘) + 𝐵𝑢(𝑘), (2.2)

𝑢 ∈ 𝒰,

where x(k) ℝn and u(k) ℝm, and A ℝn×n, B ℝn×m, are known matrices with constant

entries of corresponding entries. The cost function J(k) is linear quadratic, Linear Quadratic

Predictive Control (LQPC), with symmetric weighting matrices Q and R, where Q ≥ 0, R > 0,

and 𝒰 is an admissible control set.

HP

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𝑚𝑖𝑛𝑢0,…,𝑢𝐻𝑃−1

= ∑ 𝑥(𝑘)𝑇𝑄𝑥(𝑘) + 𝑢(𝑘)𝑇𝑅𝑢(𝑘)

𝐻𝑃−1

𝑘=0

, (2.3)

𝑠. 𝑡. 𝑥(𝑘 + 1) = 𝐴𝑥(𝑘) + 𝐵𝑢(𝑘), 𝑘 = 0,…𝐻𝑃 − 1, (2.4)

𝑢(𝑘) ∈ 𝒰, 𝑥(𝑘 + 1) ∈ 𝒳, 𝑘 = 0,… , 𝐻𝑃 − 1,

𝑥0 = 𝑥(𝑡) ≡ 𝑥(𝑘).

The future states are described as,

��(k) = 𝐺𝛥𝑈(𝑘) + 𝛤𝑥(𝑘), (2.5)

��(𝑘) = [𝑥 (𝑘 + 1)⋮𝑥 (𝑘 + 𝐻𝑃)

] = [𝐴⋮𝐴𝐻𝑃

]⏟ 𝛤

𝑥(𝑘) + [𝐵 ⋯ 0⋮ ⋱ ⋮𝐴𝐻𝑃−1𝐵 ⋯ 𝐵

]⏟

𝐺

[𝛥𝑢(𝑘)⋮𝛥𝑢(𝑘 + 𝐻𝑃 − 1)

]

⏟ 𝛥𝑈

, (2.6)

��0 = 𝛤𝑥 (𝑘). (2.7)

For regulation proposes, and considering the general case which intent to lead the state to zero,

the linear MPC without constraints solution of (2.3) is given by:

𝛥𝑈∗ = −𝐾𝑐𝑥 (𝑘) = −(𝐺𝑇𝑄𝐺 + 𝑅)−1𝐺𝑇𝑄��0 (2.8)

and implementing the first element of the optimal prediction at each sampling instant k defines a

receding horizon control law

𝑢(𝑘) = 𝛥𝑈∗(1). (2.9)

Remark that if 𝒰 and 𝒳 are polyhedral (a finite intersection of half-space), this is a Quadratic

Program, that can be can be solve fast, efficiently and reliably, using modern solver tools.

2.3.1 Linear Plant Model

For linear systems, the dependence of predictions x(k) on u(k) is linear. A quadratic

minimization cost function as (2.3) is therefore a quadratic function of the input sequence vector

u. Thus J(k) can be expressed as a function of u in the form,

𝐽(𝑘) = 𝒖𝑇(𝑘)𝐻𝒖(𝑘) + 2𝑓𝑇𝒖(𝑘) + 𝑔, (2.10)

where H is a constant positive definite (or possibly positive semi-definite) matrix, and f, g are

respectively a vector and scalar which depend on x(k). The online MPC optimization therefore

comprises the minimization over u of a quadratic objective:

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𝑚𝑖𝑛𝑢 𝒖𝑇(𝑘)𝐻𝒖(𝑘) + 2𝑓𝑇𝒖(𝑘). (2.11)

In the absence of constraints, unconstrained MPC, the optimization u*(k) = 𝑚𝑖𝑛𝐮 𝐽(𝑘) has a

closed-form solution which can be derived by considering the gradient of J with respect to u:

𝛻𝑢 𝐽 = 2𝐻𝒖 + 2𝐹𝑥(𝑘). (2.12)

Clearly 𝛻u𝐽 =0 must be satisfied at a minimum point of J, and since H is positive definite (or

positive semidefinite), any u such that 𝛻u𝐽 =0 is necessarily a minimum point. Therefore the

optimal u* is unique only if H is non-singular and is then given by,

𝒖∗(𝑘) = −𝐻−1𝐹𝑥(𝑘). (2.13)

Remark that, sufficient conditions for H to be non-singular are for example that R > 0 or Q, �� >

0 and the pair (A,B) is controllable.

If H is singular (i.e. positive semi-definite rather than positive definite), then the optimal u* is

non-unique, and a particular solution of 𝛻u𝐽 =0 has to be defined as,

𝑢(𝑘) = −𝐻†𝐹𝑥(𝑘), (2.14)

where H† is a left inverse of H (so that H†H = I).

Implementing the first element of the optimal prediction u*(k) at each sampling instant k defines

a receding horizon control law. Since H and F are constant, this is a linear time-invariant

feedback controller u(k) = KC x(k), where the gain matrix KC is the first row of −H−1F for the

single-input case (or the first nu rows for the case that u has dimension nu), i.e.

𝑢(𝑘) = 𝑢∗(𝑘|𝑘) = 𝐾𝐶𝑥(𝑘), (2.15)

𝐾𝐶 = −[𝐼𝑛𝑢 0 … 0]𝐻−1𝐹. (2.16)

Constrained MPC is used when structural limitations of the system to be controlled usually

leads to control restrictions and avoiding such limitations may cause harmful effects as unstable

cycle. However, for performance purpose, the control system should try to use the system as

close to those limits as possible, without crossing them. Therefore, MPC uses a more direct

approach by finding the optimal control in such a way that constraints are not violated.

Most typically, linear input and state constraints likewise imply linear constraints on u(k) which

can be expressed

𝐴𝑐𝒖(𝑘) ≤ 𝑏𝑐 , (2.17)

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where Ac is a constant matrix and, depending on the form of the constraints, the vector bc may

be a function of x(k). So, considering the optimization function (2.11) but now subject to linear

constraints:

𝑚𝑖𝑛𝑢 𝒖𝑇(𝑘)𝐻𝒖(𝑘) + 2𝑓𝑇𝒖(𝑘),

(2.18)

𝑠. 𝑡. 𝐴𝑐𝒖(𝑘) ≤ 𝑏𝑐 . (2.19)

This class of optimization problem is known as a quadratic programming (QP) problem, and

given that H is a positive definite matrix and the constraints are linear, it is easy to show that

(2.18) and (2.19) are a convex problem (i.e. both the objective (2.18) and constraints (2.19) are

convex functions of the optimization variable u. This kind of problem can be solved efficiently

and reliably using commercial solver and specialized algorithms.

Generally, the constraints which are applied on control input, state or output assume the

following form:

𝑢 ≤ 𝑢(𝑘) ≤ 𝑢, (2.20)

𝑥 ≤ 𝑥(𝑘) ≤ 𝑥, (2.21)

𝑦 ≤ 𝑦(𝑘) ≤ 𝑦, (2.22)

or even rate constraints:

∆𝑢 ≤ 𝑢(𝑘) − 𝑢(𝑘 − 1) ≤ ∆𝑢. (2.23)

Input constraints commonly arise as a result of actuator limits, e.g. torque saturation in d.c.

motors and flow saturation in valves and the state constraints may be active during transients,

e.g. aircraft stall speed, or in steady-state operation as a result of e.g. economic constraints on

process operation. In addition to the obvious equality constraints that the state and input should

satisfy the model dynamics, inequality constraints on input and state variables are encountered

in every control problem. While the equality constraints are usually handled implicitly (i.e. the

plant model is used to write predicted state trajectories as functions of initial conditions and

input trajectories), the inequality constraints are imposed as explicit constraints within the

online optimization problem.

However, constraints are classified as hard or soft. The hard constraints, must always be

satisfied, and when is not possible, the problem is becomes infeasible.

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Figure 2.5. Hard constraint representation (Adapted from Froisy, 1994).

On the other hand, soft constraints may be violated if necessary to avoid infeasibility, generally

with a penalization in the cost function.

Figure 2.6. Soft constraint representation (Adapted from Froisy, 1994).

Chapter 4 shows an example of hard constraints application and in Chapter 6 and 7 soft

constraints. Thus, constraints will be here generically described and exemplified.

To implement a soft constraint, allowing for example that the output variable exceeds the

constraint value in a specified value 𝜖 ≥ 0,

𝑦(𝑡 + 𝑗) ≤ 𝑦 + 𝜖(𝑡 + 𝑗),

𝜖(𝑡 + 𝑗) ≥ 0, 1 ≤ 𝑗 ≤ 𝑁𝑠𝑜𝑓𝑡 .

with 𝑁𝑠𝑜𝑓𝑡 representing the horizon where the soft constraint is considered.

Thus a new term is included in the cost function (2.18),

𝑚𝑖𝑛𝑢 𝟏

𝟐𝒗𝑇𝑯𝒗 + 𝒃

𝑇𝒗, (2.24)

with

time

time

Maximum

constraint value

Maximum

constraint value

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𝑯𝒖 = −𝑏, (2.25)

𝒗𝑇 = [𝒖𝑇 𝜖𝑇], 𝑯 = [𝑯 00 𝜆𝑟𝑰

],

𝒃𝑇= [𝒃𝑇 0], 𝜖 = [𝜖(𝑡 + 1) ⋯ 𝜖(𝑡 + 𝑁𝑠𝑜𝑓𝑡)].

Where λ𝑟 > 0 is the ponderation factor and 𝐇 the Hessian matrix. The optimization problem

must also include,

𝑦(𝑡 + 𝑗) − 𝜖(𝑡 + 𝑗) ≤ 𝑦, 𝜖 ≥ 0. (2.26)

Now, to be able to be solved as a quadratic optimization problem the constraints must be

expressed as inequalities constraints, assuming the following form:

𝑚𝑖𝑛𝑢 𝟏

𝟐𝒗𝑇𝑯𝒗 + 𝒃

𝑇𝒗, (2.27)

𝑠. 𝑡. 𝐴𝒖 ≤ 𝑐. (2.28)

In a systematic way other soft constraints can be considered in the output value,

𝑦(𝑡 + 𝑗) − 𝜖(𝑡 + 𝑗) ≤ 𝑦(𝑡 + 𝑗) ≤ 𝑦(𝑡 + 𝑗) + 𝜖(𝑡 + 𝑗), 𝑁𝑚 ≤ 𝑗 ≤ 𝐻𝑃 , (2.29)

And expressing the constraints as manipulated variables

𝑮𝒖 − 𝜖 ≤ 𝟏𝑦, (2.30)

−𝑮𝒖 − 𝜖 ≤ −𝟏𝑦, 𝜖 ≥ 0.

With 1 representing a (HP-Nm) matrix with unitary values, and G the dynamic matrix and the

incremental control vector.

To implement hard constraints on U, I

𝑈 ≤ 𝑢(𝑡 + 𝑗) ≤ 𝑈, 𝑁𝑚 ≤ 𝑗 ≤ 𝐻𝑃. (2.31)

Expressing the constraints as manipulated variables,

𝑻𝒖 ≤ 𝟏𝑈 − 1𝑢(𝑡 − 1), (2.32)

−𝑻𝒖 ≤ −𝟏𝑈 + 1𝑢(𝑡 − 1).

Where T is an upper triangular matrix with (NC×NC). Considering also hard constraints in y, the

output is written as,

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𝑦(𝑡 + 𝑗) ≤ 𝑦(𝑡 + 𝑗) ≤ 𝑦(𝑡 + 𝑗), 𝑁𝑚 ≤ 𝑗 ≤ 𝐻𝑃 , (2.33)

and once again,

𝑮𝒖 ≤ 𝟏𝑦, (2.34)

−𝑮𝒖 ≤ −𝟏𝑦.

Supposing a set of constraints acting over a process, where the control signal U amplitude, the

actuator slew rate u and output signal y are limited. These constraints can be expressed as,

𝑈 ≤ 𝑢(𝑡) ≤ 𝑈 ∀ 𝑡,

𝑢 ≤ 𝑢(𝑡) − 𝑢(𝑡 − 1) ≤ 𝑢 ∀ 𝑡, (2.35)

𝑦 ≤ 𝑦(𝑡) ≤ 𝑦 ∀ 𝑡,

Considering that the process has m inputs and n outputs with constraints acting along a horizon

HP, (2.35) can be reformulated

𝟏𝑈 ≤ 𝑻𝒖 + 𝑢(𝑡 − 1) ≤ 𝟏𝑈 ∀ 𝑡,

𝟏𝑢 ≤ 𝒖 ≤ 𝟏𝑢 ∀ 𝑡, (2.36)

𝟏𝑦 ≤ 𝑮𝒖 ≤ 𝟏𝑦 ∀ 𝑡,

where 1 is a matrix (HP×n)×m with HPm×m identity matrices, and T is a lower triangular matrix

where the non-null inputs are identity matrices with (m×m), and writing the constraints in a

condensed form, results in,

𝐴𝒖 ≤ 𝑐,

with,

𝑨 =

[

𝑻−𝑻

𝑰𝐻𝑃×𝐻𝑃−𝑰𝐻𝑃×𝐻𝑃

𝑮−𝑮 ]

; 𝒄 =

[ 𝟏𝑈 − 𝟏𝑢(𝑡 − 1)−𝟏𝑈 + 𝟏𝑢(𝑡 − 1)

𝟏𝑢−𝟏𝑢

𝟏𝑈−𝟏𝑈 ]

. (2.37)

The QP solution can be obtained using a modified Lemke’s method (Camacho, 1993; Igreja and

Cruces, 2002).

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2.3.2 Nonlinear Plant Model

Although the majority of processes are inherently nonlinear, most of the applications use linear

dynamic models. Several reasons are behind this fact, or because empirical linear models can be

easily identified because mostly process work nearby a desire operation point, or because linear

models may present sufficient precision when in presence of high quality the feedback

measures. Linear models may use quadratic objective functions that are simply solve with LQ

convex programming which provide a solution that should converge to the optimal criterion.

The use of nonlinear models in MPC is motivated by the need to improve the control of

processes with robust linearity’s through by improving the prediction quality.

Thus, MPC has a large population of potential applications even for nonlinear systems,

according to (Allgöwer et al., 2004), the key characteristics and properties of NMPC are:

NMPC allows the direct use of nonlinear models for prediction;

NMPC allows the explicit consideration of state and input constraints;

In NMPC a specified time domain performance criteria is minimized on-line;

In NMPC the predicted behaviour is in general different from the closed-loop

behaviour;

For the application of NMPC typically a real-time solution of an open-loop optimal

control problem is necessary;

To perform the prediction the system states must be measured or estimated;

The optimization problem is nonconvex, more difficult to solve than QP;

The computation time increases because the difficulty to find the solution of the

optimisation problem;

If a nonlinear prediction model is employed, then due to the nonlinear dependence of the state

predictions x(k) on u(k), the MPC optimization problem is significantly harder than for the

linear model case. This is because the cost in equation (2.3), which can be written as J(u(k),

𝑥(𝑘)), and the constraints, g(u(k), x(k)) ≤ 0, are in general nonconvex functions of u(k), so that

the (2.3) optimization problem,

𝑚𝑖𝑛𝒖 𝐽(𝒖; 𝑥(𝑘)),

(2.38)

𝑠. 𝑡. 𝑔(𝒖; 𝑥(𝑘)), (2.39)

becomes a nonconvex nonlinear programming (NLP) problem. As a result there will in general

be no guarantee that a solver will converge to a global minimum of (2.38) and the times

required to find even a local solution are typically orders of magnitude greater than for QP

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problems of similar size. Unlike QP solvers, the computational loads of solvers for nonlinear

programming problems are strongly problem-dependent.

2.3.3 Generalized Predictive Control

Another similar MPC strategy that will be used in Chapter 4, is Generalized Predictive Control.

(GPC). GPC was developed by (Clarke et al., 1987) and is a popular form of MPC. In the

original version of GPC, stability was not guaranteed because of using finite horizon. New

versions of GPC were based on the idea that the stability of GPC could be guaranteed if in the

last part of the prediction horizon the future outputs are constrained at the desired set point, and

also the prediction horizon is properly selected. The well-known example for this category is

Stabilizing Input/Output Receding Horizon Control (SIORHC). The GPC controller uses a

Controlled Auto-Regressive Integrated Moving Average (CARIMA) model as presented in the

next difference equation,

𝐴(𝑞−1)𝛥𝑦(𝑡) = 𝑞−𝑑𝐵(𝑞−1)𝛥𝑢(𝑡) + 𝐶(𝑞−1)𝜉(𝑡), (2.40)

where y(t) is the process output, u(t) is the control variable, d is the delay, (t) is the measure

noise (perturbations, model errors). The GPC control law is obtained with the minimization of

the following equation,

𝐽𝐺𝑃𝐶 = ∑ [𝑦(𝑡 + 𝑗) − 𝑦𝑟(𝑡 + 𝑗)]2

𝐻𝑃

𝑗=𝑁𝑚

+∑𝑅𝛥𝑢2(𝑡 + 𝑗 − 1),

𝑁𝐶

𝑗=1

(2.41)

where R is the control weight, Nm is the minimum horizon, specifying the beginning of the

horizon in the cost function from which point the output error is taken into account, and HP

represents the prediction horizon, specifying the last output error that is taken into account. NC

is the control horizon, y(t+j) and yr(t+j) are the output and reference signal, u(t+j–1) is the

control signal increment at (t+j–1). The control weight and control horizon are the main two

tunings GPC parameters that allows obtaining different predictive controllers in order to adjust

them to the desire control plant (Clarke et al., 1987). Remark that, the control action affects the

process output only after the delay, it is reasonable to choose the minimum horizon higher or

equal to the process delay. If the process delay is unknown then, the delay can be set to one and

the minimum horizon to zero without the loss of stability. The choice of the minimum horizon

can be interesting in case of non-minimum phase processes.

Consider the polynomial,

𝐶(𝑞−1) = 𝐴(𝑞−1)𝛥𝐸𝑗(𝑞−1) + 𝑞−𝑗𝐹𝑗(𝑞

−1), (2.42)

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where,

𝐸𝑗(𝑞−1) = 1 + 𝑒1𝑞

−1+ . . . +𝑒𝑛𝑒𝑞−𝑛𝑒 ,

𝐹𝑗(𝑞−1) = 𝑓0 + 𝑓1𝑞

−1+ . . . +𝑓𝑛𝑓𝑞−𝑛𝑓 ,

(2.43)

ne = j –1; nf = max(na, nc – j),

are stablished knowing j and A(q–1) e C(q–1).

By manipulating the model equation (2.40) and (2.42), equation (2.46) can be obtained,

𝑦(𝑡 + 𝑗) =𝐹𝑗(𝑞

−1)

𝐶(𝑞−1)𝑦(𝑡) +

𝐺𝑗′(𝑞−1)

𝐶(𝑞−1)𝛥𝑢(𝑡 + 𝑗 − 𝑑) + 𝐸𝑗(𝑞

−1)𝜉(𝑡 + 𝑗), (2.44)

with,

𝐺𝑗′(𝑞−1) = 𝐸𝑗(𝑞

−1)𝐵(𝑞−1). (2.45)

The noise is uncorrelated from the measurable signals in instant t, so the output prediction can

be written for (t + j) as,

𝑦 (𝑡 + 𝑗) =𝐹𝑗(𝑞

−1)

𝐶(𝑞−1)𝑦(𝑡) +

𝐺𝑗′(𝑞−1)

𝐶(𝑞−1)𝛥𝑢(𝑡 + 𝑗 − 𝑑), (2.46)

with,

𝐺𝑗′(𝑞−1) = 𝐶(𝑞−1)𝐺𝑗(𝑞

−1) + 𝑞−𝑗��𝑗(𝑞−1), (2.47)

and substituting in (2.44),

𝑦 (𝑡 + 𝑗) =𝐹𝑗(𝑞

−1)

𝐶(𝑞−1)𝑦(𝑡) +

��𝑗(𝑞−1)

𝐶(𝑞−1)𝛥𝑢(𝑡 − 𝑑)

⏟ 𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒 𝑖𝑛𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛 𝑎𝑡 𝑡 𝑖𝑛𝑠𝑡𝑎𝑛𝑡

+ 𝐺𝑗(𝑞−1)𝛥𝑢(𝑡 + 𝑗 − 𝑑).⏟

𝑓𝑢𝑡𝑢𝑟𝑒

(2.48)

From (2.48) the effect of the past and future control actions, can be separated,

𝑦 (𝑡 + 𝑗/𝑡) =𝐹𝑗(𝑞

−1)

𝐶(𝑞−1)𝑦(𝑡) +

��𝑗(𝑞−1)

𝐶(𝑞−1)𝛥𝑢(𝑡 − 𝑑) (2.49)

Equation (2.46) can be represented in vectorial form,

�� = 𝐺𝛥𝑈 + 𝑓 (2.50)

With f formed with the free responses,

𝑓 = [𝑦 (𝑡 +𝑁𝑚𝑡) 𝑦 (𝑡 + 𝑁𝑚 +

1

𝑡… 𝑦 (𝑡 +

𝐻𝑃𝑡)]𝑇

, (2.51)

and

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𝛥𝑼 = [𝛥𝑢(𝑡) 𝛥𝑢(𝑡 + 1) … 𝛥𝑢(𝑡 + 𝑁𝐶 − 1)]𝑇 , (2.52)

where,

�� = [𝑦 (𝑡 + 𝑁𝑚) 𝑦 (𝑡 + 𝑁𝑚 + 1) … 𝑦 (𝑡 + 𝐻𝑃)]𝑇 , (2.53)

G =

[ 𝑔𝑁𝑚−𝑑 … 𝑔0 0 0 ⋯ 0

𝑔𝑁𝑚−𝑑+1 … 𝑔1 𝑔0 0 ⋯ 0

⋮ ⋱ ⋱ ⋮⋮ ⋱ 𝑔0⋮ … ⋮𝑔𝐻𝑃−𝑑 𝑔𝐻𝑃−𝑑−1 … 𝑔𝐻𝑃−𝑁𝐶−𝑑+1]

, (2.54)

with G (𝐻𝑃 – Nm + 1)× NC dimension.

GPC cost function can also be presented in vectorial form,

𝐽𝐺𝑃𝐶 = [�� − 𝑌𝑟]𝑇[�� − 𝑌𝑟] + 𝑅𝛥𝑈

𝑇𝛥𝑈, (2.55)

where

𝑌𝑟 = [𝑦𝑟(𝑡 + 𝑁𝑚) 𝑦𝑟(𝑡 + 𝑁𝑚 + 1) … 𝑦𝑟(𝑡 + 𝐻𝑃)]𝑇. (2.56)

Thus, (2.55) is minimized obtaining the follow control law,

𝛥𝑈 = [𝐺𝑇𝐺 + 𝑅𝐼]−1𝐺𝑇[𝑌𝑟 − 𝑓]. (2.57)

Being GPC a receding horizon controller, only the first element of the calculated control signal

sequence is to be applied on the process. The procedure of minimization of the cost function is

repeated in the next sampling instant. The applied control signal is:

𝑢(𝑡) = 𝑢(𝑡 − 1) + ∆𝑢(𝑡). (2.58)

So, GPC allows threating process with unknown or varying delays, constrained systems,

nonlinearities, non-minimum phase processes as well open-loop unstable plants (Clarke et al.,

1987b). The GPC control structure is presented in Figure 2.7.

Figure 2.7. GPC control structure.

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With M

𝑀 = [1 0 … 0][(𝐺𝑇𝐺 + 𝛬𝐼)−1𝐺𝑇], (2.59)

where 𝑀 = [𝑚𝑁𝑚 𝑚𝑁𝑚+1 … 𝑚𝐻𝑃].

So, the control applied to the process can be written as,

𝛥𝑢(𝑡) = 𝑀[𝑌𝑟 − 𝑓]. (2.60)

According Figure 2.7, the control law is given by,

𝑅(𝑞−1)𝛥𝑢(𝑡) = 𝑇(𝑞−1)𝑦𝑟(𝑡 + 𝐻𝑃) − 𝑆(𝑞−1)𝑦(𝑡), (2.61)

where

𝑅(𝑞−1) = 𝐶(𝑞−1) + 𝑞−𝑑 ∑ 𝑚𝑗��𝑗

𝐻𝑃

𝑗=𝑁𝑚

(𝑞−1), (2.62)

𝑆(𝑞−1) = ∑ 𝑚𝑗

𝐻𝑃

𝑗=𝑁𝑚

𝐹𝑗(𝑞−1), (2.63)

𝑇(𝑞−1) = 𝐶(𝑞−1) ∑ 𝑚𝐻𝑃+𝑁𝑚−𝑗

𝐻𝑃

𝑗=𝑁𝑚

𝑞−(𝑗−𝑁𝑚), (2.64)

nr = 𝐻𝑃 – Nm; ns = max(na, nc – 𝐻𝑃) and nt = max(nc, nb).

Substituting (2.61) in (2.40),

𝑦(𝑡) =[𝑞−𝑑𝐵(𝑞−1)𝑇(𝑞−1)]𝑦𝑟(𝑡 + 𝑁2)

[𝐴(𝑞−1)𝛥𝑅(𝑞−1) + 𝑞−𝑑𝐵(𝑞−1)𝑆(𝑞−1)]+

𝐶(𝑞−1)𝑅(𝑞−1)𝜉(𝑡)

[𝐴(𝑞−1)𝛥𝑅(𝑞−1) + 𝑞−𝑑𝐵(𝑞−1)𝑆(𝑞−1)] (2.65)

With (2.65), the closed loop characteristic polynomial is calculated by,

𝑃𝑚𝑓(𝑞−1) = 𝐴(𝑞−1)𝛥𝑅(𝑞−1) + 𝑞−𝑑𝐵(𝑞−1)𝑆(𝑞−1). (2.66)

As mentioned, the first generation in the MPC family, such as DMC, IDCOM and GPC used a

finite prediction horizon. This feature made it possible to incorporate constraints in the control

strategy, a capability that is not supported by infinite horizon LQ control. Initially in GPC,

because of using finite horizon, stability was not guaranteed in his original version. But later,

this issue was overcome with the idea that the stability of GPC could be guaranteed if in the last

part of the prediction horizon the future outputs are constrained at the desired set point and the

prediction horizon is properly selected. So, the stability weaknesses of the first generation were

overcome with the second generation with these two methods that are the most popular in this

category, the SIORHC (Mosca et. al 1990), or Constrained Receding Horizon Predictive

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Control (CRHPC) and Stable Generalised Predictive Control (SGPC). SIORCH optimize a

quadratic function over a prediction horizon subject to the condition that the output matches the

reference value over a further constraint range.

Another kind of adaptive predictive controller algorithm is Multistep Multivariable Adaptive

Regulator, MUSMAR (Greco et al., 1984) is a data driven algorithm designed for the adaptive

regulation of linear Autoregressive–Moving-Average Model with exogenous inputs model

(ARMAX) plants. This algorithm combines several features, the optimization of a receding

horizon quadratic cost, it assumes a constant feedback over the prediction horizon, the cost

function is minimized based on predictive models for both plant input and output signals and the

estimation of the predictors and the data are separate.

This algorithm possesses attractive local self-optimizing properties and was extendedly studied

during the eighties and nineties years of the last century (Mosca at al., 1989; Rato et al., 1997)

and successfully applied in recent years in many areas (Nunes, et al., 2007).

2.3.4 Stability and Feasibility

In this work, feedback stability is provided by choosing a sufficiently long predictive horizon

and proven by results. Feasibility is achieved by the use of soft constraints (5.1) in the

optimization problem formulation.

Table 2.1. Simulation parameters for the several prediction horizons

Parameter A1 Units

𝛯 1

5000

Φ 200

1

Req 50 ºC/kW

Ceq 9.2103 kJ/ºC

To exemplify, several predictive horizons were chosen to demonstrate the influence of this

parameter. The simulation time was also counted to evaluate the system performance under the

several HP chosen, 1, 6, 12 and 24h. The simulations were made for one house in the same

conditions used in Chapter 5, using optimization problem (5.1) and the dynamical model (3.1).

The used parameters are described in Table 2.1 and the obtained results in Figure 2.9 to Figure

2.11. It is considered that the system knows the existence of load disturbances, Figure 2.8,

inside the selected HP. Simulations were made in an Intel Core 1.59GHz, 2,0GB of RAM

machine.

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Figure 2.8. Disturbance load profile in the several prediction horizons.

Figure 2.9. Indoor temperature profile for the several prediction horizons.

Figure 2.10. Power profile for the several prediction horizons.

0 5 10 15 20-0.5

0

0.5

1

1.5

2

Time (h)

Pow

er

(kW

)

Disturbance Load (kW)

0 5 10 15 2021

22

23

24

25

26

27

28

Time (h)

Tem

pera

ture

(ºC

)

Temp. Max.

Temp. Min.

Indoor Temp HP=1.

Indoor Temp HP=6.

Indoor Temp HP=12.

Indoor Temp HP=24.

0 5 10 15 20-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Time (h)

Pow

er

(kW

)

Power Max.

Power Min.

Control Input HP=1

Control Input HP=6

Control Input HP=12

Control Input HP=24

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Figure 2.11. Consumption profile for several prediction horizons.

As can be seen in Figure 2.9, with HP=1 the system becomes instable, the indoor temperature

diverge from the chosen comfort zone because with this horizon the power consumption is

almost null. The indoor temperature and power profiles are similar with the others HP, but

remark that, with HP=24, the system is able to anticipate sooner all the disturbances and

constraints and by that reason the power consumption is higher in order to also maintain the

temperature inside bounds. It can be seen that the compromise between comfort and

consumption is notorious, the controllers are always attempting to accomplish both constraints,

but when is not possible, it compensates with one inside range and the other outside. The

application of soft constraints allows this behaviour and the problem feasibility.

As expected, Table 2.2 shows that higher prediction horizons has the drawback of higher

computational efforts, the compromise between anticipation, feasibility and computational

efforts must be taken in account when the parameters are chosen.

Table 2.2. Computational efforts under several prediction horizons

HP (h) Computational effort (s)

1 2,8

6 4,4

12 52,5

24 289,5

2.3.5 Centralized MPC

The continuous instrumentation development associated to the need of improvements in

processes and environmentally conscious solutions has made the process control become even

0 5 10 15 200

2

4

6

8

10

12

14

Time (h)

Pow

er

(kW

h)

HP=1

HP=6

HP=12

HP=24

LITERATURE REVIEW

36

more complex. With this, the implementation and maintenance of centralized MPC algorithms

have become an important issue and often complicated to treat. Some of the major obstacles

encountered in the use of advanced control techniques, such as MPC, are the difficulty of

communication between sensors and processing units in geographically distributed systems and

computational limitations for some optimization problems. Although, for large and

geographically distributed systems, the two mostly used control strategies are centralized or

decentralized. Centralized control can coordinate subsystems but may suffer from the curse of

dimensionality and failures in the central control unit. In general, in most of the applications,

MPC is implemented in a centralized scheme, where the complete system is modelled and all

the control inputs are computed in one optimization problem, Figure 2.12.

Figure 2.12. Centralized MPC architecture (Scattolini, 2009).

The overall system model can be represented as a discrete, linear time invariant (LTI) model

with the form,

𝑥(𝑘 + 1) = 𝐴𝑥(𝑘) + 𝐵𝑢(𝑘), (2.67)

𝑦(𝑘) = 𝐶𝑥(𝑘) ,

in which,

𝐴 =

[ 𝐴11 𝐴12 … 𝐴1𝑁𝑠⋮ ⋮ ⋱ ⋮𝐴𝑖1 𝐴𝑖2 … 𝐴𝑖𝑁𝑠⋮ ⋮ ⋱ ⋮

𝐴𝑁𝑠1 𝐴𝑛𝑠2 … 𝐴𝑁𝑠𝑁𝑠]

, 𝐵 =

[ 𝐵11 𝐵12 … 𝐵1𝑁𝑠⋮ ⋮ ⋱ ⋮𝐵𝑖1 𝐵𝑖2 … 𝐵𝑖𝑁𝑠⋮ ⋮ ⋱ ⋮

𝐵𝑁𝑠1 𝐵𝑁𝑠2 … 𝐵𝑁𝑠𝑁𝑠]

,

𝐶 = [

𝐶11 0 … 00 𝐶22 ⋱ 0⋮ ⋮ ⋱ ⋮0 … … 𝐶𝑁𝑠𝑁𝑠

],

(2.68)

𝑢 = [𝑢1′ … 𝑢𝑁𝑠

′ ]′ ∈ ℝ𝑚,

𝑥 = [𝑥1′ … 𝑥𝑁𝑠

′ ]′ ∈ ℝ𝑛, (2.69)

MPC

Subsystem

1

Subsystem

2

u1

u2

System

y1

y2

x1 x2

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37

𝑦 = [𝑦1′ … 𝑦𝑁𝑠

′ ]′ ∈ ℝ𝓏 .

For each subsystem i= 1, 2,…, Ns, the (ui, xi,, yi) represents the subsystem input, state and

output vector respectively. Thus, in the centralized MPC framework, the following optimization

problem is solved,

𝑚𝑖𝑛𝑥,𝑢

𝐽(𝒙, 𝒖; 𝑥(𝑘)) =∑𝑤𝑖𝑖

𝐽𝑖(𝒙𝑖 , 𝒖𝑖; 𝑥𝑖(𝑘)), (2.70)

𝑠. 𝑡. 𝑥(𝑘 + 1) = 𝐴𝑥(𝑘) + 𝐵𝑢(𝑘), (2.71)

𝑢𝑖(𝑘) ∈ 𝒰𝑖 𝑖 = 1, … , 𝑁𝑆,

𝐽𝑖 =∑𝐿𝑖

𝑁

𝑗=1

(𝑥𝑖(𝑘 + 𝑗), 𝑢𝑖(𝑘 + 𝑗 − 1)),

𝐿𝑖 =1

2[𝑥𝑖𝑇𝑄𝑖𝑥𝑖 + 𝑢𝑖

𝑇𝑅𝑖𝑢𝑖].

Where 𝑤𝑖 > 0,∑𝑤𝑖 = 1, 𝑄𝑖 ≥ 0 , 𝑅𝑖 > 0 and (𝐴𝑖, √𝑄𝑖) detectable and 𝑥𝑖(𝑘) given.

For any system, centralized MPC achieves the best attainable performance (Pareto optimal) as

the effect of interconnections among subsystems are accounted for exactly. Additionally,

existent conflicts among controller objectives are solved optimally (Venkat et al., 2008).

Normally, centralized MPC can be used in the form of a supervisory controller that have access

to all variables in the network and that determines actions for all actuators. Due to practical and

computational issues the implementing a centralized controller may not be feasible. Individual

hubs may not want to give access to their sensors and actuators to a centralized authority and

even if they would allow a centralized authority to take over control of their hubs, this

centralized authority could have computational problems with respect to required time when

solving the resulting centralized control problem. This approach is ideal for small scale systems,

but when the control and optimization problem involves a large scale system the conventional

approach requires the decomposition of the global system into smaller subsystems.

2.3.6 Decentralized MPC

Alternatively, decentralized control uses a distributed approach that decomposes a large

optimization problem in small ones that can be solve by agents, preserving or even improving

the final performance (Camponogara et al., 2002). Each agent solves its sub-problem and

computes its own control actions, taking in to account possible mutual influences between other

LITERATURE REVIEW

38

neighbouring agents. Thus, decentralized control is desirable for being scalable and robust but

fails to account for the mutual influence among neighbouring subsystems that can have long-

range effects. The key feature of a decentralized control framework is that there is no

communication between the different local controllers. While there are some important reviews

on decentralized control see (Christofides et al., 2013) for a tutorial review. A schematic for

decentralized MPC architecture, with two subsystems with state coupling, is shown in Figure

2.13.

Figure 2.13. Decentralized MPC architecture (Scattolini, 2009).

Note that strong interactions between different subsystems may prevent one from achieving

stability and desired performance with decentralized control. So, in order to achieve closed-loop

stability as well as performance in the development of decentralized MPC algorithms, the

interconnections between different subsystems are assumed to be weak or negligible, and are

considered as disturbances which can be compensated through feedback so they are not

involved in the controller formulation explicitly. Thus, the effect of external subsystems on the

local subsystem is omitted in this modelling framework. Remark that, when the above

assumption is not valid it may lead to a reduced control performance. Assuming a block

diagonal structure for the overall dynamic system, each subsystem is modelled by

𝑥𝑖(𝑘 + 1) = 𝐴𝑖𝑖𝑥𝑖(𝑘) + 𝐵𝑖𝑖𝑢𝑖(𝑘), (2.72)

𝑦𝑖(𝑘) = 𝐶𝑖𝑖𝑥𝑖(𝑘) 𝑖 = 0, … , 𝑁𝑆.

In the decentralized MPC framework, each subsystem MPC solves the following optimization

problem,

𝑚𝑖𝑛𝑥,𝑢

𝐽𝑖(𝒙𝑖 , 𝒖𝑖; 𝑥𝑖(𝑘)), (2.73)

𝑠. 𝑡. 𝑥𝑖(𝑙 + 1|𝑘) = 𝐴𝑖𝑖𝑥𝑖(𝑙|𝑘) + 𝐵𝑖𝑖𝑢𝑖(𝑙|𝑘), 𝑘 ≤ 𝑙, (2.74)

𝑢𝑖 ∈ 𝒰𝑖 , 𝑘 ≤ 𝑙.

MPC 1

MPC 2

Subsystem

1

Subsystem

2

u1

u2

System

y1

y2

x2 x1

LITERATURE REVIEW

39

Each decentralized MPC solves an optimization problem to minimize its local cost function.

2.3.7 Distributed Model Predictive Control

The MPC have also evolved as a distributed systems control methodology (Negenborn, et al.,

2006; Scattolini, 2009; Igreja et al., 2012). Distributed or decentralised Model Predictive

Control allows the distribution of decision-making while handling constraints in a systematic

way. DMPC algorithms, offers the same features of MPC but have the advantage of supporting

the distribution of sensing and control using local controllers/agents that cooperate by

exchanging information to decide their control actions. This is the reason why it was the chosen

method to deal with this kind of system. These DMPC infrastructures are suitable to use in a

MAS (see Chapter 2.4) framework where, in a distributed environment, several agents

employing individually a MPC control strategy are able to interact and receive influence from

neighbour subsystems, exchange predictions on their future state and incorporate this

information into their local MPC problems.

Large scale interconnected systems, such as power systems, water distribution, traffic systems,

etc, require control techniques adjusted to the distributed nature of the system, as, decentralized

or distributed control (Krogh, 2001). However, in decentralized MPC approach, the information

exchange between subsystems is ignored and each subsystem is constructed with its individual

control system forming a traditional centralized control scheme. This decentralized control

architecture may result in poor system-wide control performance if the subsystems interact

significantly (Venkat, et al., 2006). In distributed MPC, there is not a single MPC controller but

instead there are multiple MPC controllers, each for a particular system. Typically, there is

dynamical interaction among the systems that the individual controllers consider. Each of the

controllers adopts the MPC strategy as outlined above for controlling its system but now not

only considering dynamics, constraints, objectives, and disturbances of the subsystem under

consideration but also considers the interactions among the systems. Each local controller solves

an MPC problem based on local information and may hereby share information with the other

controllers to improve the overall performance.

Figure 2.14 represent a simple distributed control system where it is assume that local regulators

interact between them, obtaining by this way some information on the behaviour of the others.

This information is normally related with future predicted control or state variables computed

locally, so that any local regulator can predict the interaction effects over the considered

prediction horizon.

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40

Figure 2.14. Distributed MPC architecture (Scattolini, 2009).

The generalized optimal state-input trajectory for (𝒙𝑖𝑝, 𝒖𝑖𝑝) for subsystem i (i=1,2,…Ns) at

iteration p is obtained as the solution to the optimization problem,

𝑚𝑖𝑛𝒙𝒊,𝒖𝒊

𝐽𝑖(𝒙𝑖 , 𝒖𝑖; 𝑥𝑖(𝑘)), (2.75)

𝑠. 𝑡. 𝑥𝑖(𝑙 + 1|𝑘) = 𝐴𝑖𝑖𝑥𝑖(𝑙|𝑘) + 𝐵𝑖𝑖𝑢𝑖(𝑙|𝑘) +∑[𝐴𝑖𝑗𝑥𝑗𝑝−1(𝑙|𝑘) + 𝐵𝑖𝑗𝑢𝑗

𝑝−1(𝑙|𝑘)]

𝑗≠𝑖

, 𝑘 ≤ 𝑙 (2.76)

𝑢𝑖 ∈ 𝒰𝑖 , 𝑘 ≤ 𝑙, 𝑖 = 0, … , 𝑁𝑆.

When moving from a centralized MPC to a distributed MPC setting, several key concepts

become relevant. In a distributed MPC setting, a system or subsystem refers to the entity being

controlled by the controller. The overall system is the combination of all systems or subsystems

under control merged into one large-scale system. The notions of global versus local distinguish

between the overall system and the system or subsystem under control by a particular controller.

Hence, frequently appearing concepts are local objectives, local dynamics, local constraints, and

local disturbances. The terms interconnecting and shared are often used in combination with the

terms variables and constraints to denote explicitly those components that represent the

connections or couplings between different systems. In a distributed setting, a particular

controller has neighbours, or neighbouring controllers. The neighbours are those controllers that

control systems that are coupled or influence the system under control by this particular

controller. Communication takes places among the controllers, which can exchange

information, for example, regarding local states, local objectives, and/or local constraints.

Information can then be taken into account by the controllers to implement a coordination or

negotiation process. The controllers can be structured in control layers or levels, leading to a

hierarchical control structure. Here, typically at higher levels, controllers consider slower time

scales and larger systems in a more abstract way, whereas at lower levels, controllers consider

faster time scales and smaller systems in a more detailed way. The potential of distributed MPC

lies in the unique combination of the strengths of MPC (namely, feedback with feed-forward

MPC 1

MPC 2

Subsystem

1

Subsystem

2

u1

u2

y1

y2

System

x2 x1

LITERATURE REVIEW

41

control in a receding horizon fashion, multi-objective optimization, and explicitly handling of

constraints) with the negotiation and coordination possibilities provided by communication. The

role played by communication in this context is essential. For example, the distinction between

decentralized and distributed MPC lies in whether or not the controllers actively communicate

with one another to determine actions. In decentralized control architecture, there is no direct

communication between controllers; controllers take into account the influence of neighbouring

systems only by responding to the dynamics of the systems they are controlling. This constraint

typically limits the performance that the decentralized MPC control scheme can achieve. In fact,

in a decentralized MPC scheme, controllers may be opposing one another’s actions, even

though they may not have the intention to do so. In a distributed MPC setting, such a situation

can be prevented because the controllers can communicate about what actions they are going to

take when and obtain agreement on an optimal timing.

In summary, DMPC is an evolving technology that advocates the distribution of sensing and

control while preserving the same features of standard MPC, namely, the use of a prediction

model and the explicit handling of constraints (Saluje et al., 2011).

As mentioned DMPC strategies can be characterized by the type of couplings or interactions

assumed between constituent subsystems (Trodden & Richards 2010), (Keviczky, et al., 2006).

For example, dynamically coupled systems can be seen in several contributions (Doan, et al.,

2009; Camponogara et al. 2002; Ling, et al., 2005; Dunbar 2007; Giovanini, et al., 2007;

Venkat, et al., 2008, Alessio, et al., 2011).

Another common application of DMPC is on subsystems where the states are not dynamically

coupled but are coupled in their objective functions. A DMPC coupling via the cost function

(Wang, et al., 2010), considers the DMPC of systems with interacting subsystems having

decoupled dynamics and constraints but coupled costs. Works with similar approaches can be

seen in literature (Raffard, et al., 2004; Franco, et al. 2007).

Other different strategy involves subsystems sharing coupled constraints and many approaches

have been presented in the literature. In Riggs, et al., 2010 is establish an algorithm where an

optimization problem is performed by different subsystems with their own objective functions

and local constraints, but share a common coupled constraint which limits the behaviour of the

independent systems.

Biegel, et al.,(2014) presents a dual decomposition as a means to coordinate a number of

subsystems coupled by state and input constraints where each subsystem have a model

predictive controller while, a centralized entity manages the subsystems via prices associated

with the coupling constraints. This system allows coordination of all the subsystems without the

need of sharing local dynamics, objectives and constraints.

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42

Another approach (Müller, et al., 2012) presents a framework for DMPC of discrete-time

nonlinear systems with decoupled dynamics, but subject to coupled constraints and a common,

cooperative task. Each system exchange information about is predicted trajectories with its

neighbours in order to be able to achieve the common objective and to satisfy the coupling

constraints. Systems coupled by constraints can be seen in (Waslander, et al., 2004; Keviczky,

et al., 2006; Richards & How 2007; Kuwata et al., 2007).

Due to its features, DMPC (Camponogara, et al., 2002) has been developed for application to

large-scale systems, namely as process control (Borrelli, et al., 2005), chemical plants (Venkat,

et al., 2004) and or teams of vehicles (Riggs, et al., 2010) (Kuwata, et al., 2007), in which

control by a single centralised agent would require excessive communication, computation and

reliance on a single processor.

Due the characteristics mentioned above DMPC, are been applied in many distributed

applications, and several approaches and architectures to this control scheme are emerging.

Some studies are applying MPC to reduce and optimize the energy consumption in the

residential sector, namely, to deal with temperature set points regulations (Morosan, et al., 2010;

Bălan, et al., 2009; Freire, et al., 2008). In particular Freire, et al., (2008), with a DMPC control

algorithm based a modified version of Benders’ decomposition the control problem objective is

to minimize the heating energy bills while maintaining a certain indoor thermal comfort.

A DMPC scheme with stability constraint (DMPC-SC), where controllers to obtain coordination

with each other, spread information about their predictions and their local state measurements

and use them in their local computations, is described in (Krogh, 2001).

For serially connected processes, (Zhang & Li, 2007), proposed a networked MPC scheme with

neighbourhood optimization where each MPC unit receives information about the foreseeable

action for its neighbour sub-processes. Therefore, the exchange information allows cooperation

between subsystems and the optimizer to generate a suitable control decision for each sub-

process.

Bendtsen et al., (2010), proposed hierarchical approach, consisting of a three-level structure

with a high level MPC controller, a second level of so-called aggregators, controlled by an

online MPC-like algorithm, and a lower level of autonomous units. The approach is motivated

by smart-grid electric power production and consumption systems, being the goal to

accommodate load variations on the grid, arising from varying consumption and natural

variations in power production, e.g. from wind turbines.

Stewart et al., (2010) also proposed a hierchical cooperative distributed MPC without requiring

additional coordinating controllers. The head of each subsystem performs a small additional

LITERATURE REVIEW

43

calculation at each pack of information exchange to reduce the volume of communication and to

hide input trajectories between neighbours.

Negenborn, (2007), develop a multi-agent MPC control structure with applications to control

problems in power networks. The control agent uses the prediction model to predict the

behaviour of the system under various manners, and establish the actions that optimize the

behaviour of the system and minimize the costs existing in the objective function.

Ventak (2006), proposed, a cooperative distributed MPC framework, where the objective

functions of the local MPCs are modified to achieve global control objectives.

Besides the advantages above mentioned, DMPC seems to be the right approach to deal with

complex distributed systems, they can take into account all available information and that it can

therefore anticipate undesirable situations in the future at an early stage.

As mentioned, for the control problem of large-scale systems, centralized model predictive

control is impractical due to a number of limitations, including the computational efforts and

limited communication, and due this fact, more research is needed in distributed and

hierarchical model predictive control methods in order to develop new methods and algorithms

to implement in large-scale systems. Smart grids are characterized by complex dynamics and

mutual influences between all the involved identities and the algorithms should be able to deal

with couplings in the dynamics and the constraints between subsystems, and guarantee

feasibility and stability of the closed-loop system.

Instead, DMPC distributes control decision-making among agents corresponding to the different

subsystems making up the whole. The challenge is then how to coordinate efforts to ensure that

the distributed decisions lead to constraint satisfaction, feasibility and stability of the overall

closed-loop system. Several strategies for DMPC have been presented in the literature, and

many theoretical results exist, including those for feasibility and stability; see Scattolini (2009)

for a comprehensive survey. The approaches are broadly divisible by the type of couplings or

interactions assumed between constituent subsystems. The degree of coupling among the

subsystems varies. In the most complex situation, the dynamics or/and constraints of

subsystems are coupled. The method presented assumes the latter type of coupling, and has

agents update their plans one at a time, with iteration, to ensure coupled constraint satisfaction;

however, unlike other methods, it also permits a flexible order of updating.

Robustness to disturbances is a key challenge in the development of MPC (Mayne et al., 2000),

and is harder still when control decision-making is decentralised; few DMPC schemes in the

literature offer robustness. In Richards and How (2007), robust feasibility and stability are

guaranteed by updating each subsystem’s plan in a sequence, subject to tightened constraints,

and while ‘freezing’ the plans of others. Alternative approaches include treatment of

LITERATURE REVIEW

44

interconnected subsystems’ state trajectories as bounded uncertainties, and using min-max

optimization (Jia & Krogh 2002) – though the complexity issues with such an optimisation

method are well documented (Mayne et al., 2000). Using the comparison model approach to

robustness (Fukushima & Bitmead 2005), another distributed method (Kim & Sugie 2005) uses

worst-case predictions of state errors, determined based on a robust control Lyapunov function,

and tightens constraints accordingly. Magni & Scattolini (2006) propose a robust stable

decentralised algorithm for non-linear dynamically coupled systems, with no information

exchange between agents, although for an asymptotically decaying disturbance.

The new algorithm in this thesis exploits this feature to achieve flexibility in communication.

An additional advantage of this approach is that the optimisation involves only the nominal

system dynamics, avoiding the large increase in computational complexity associated with the

inclusion of uncertainty in the optimisation as mentioned in (Scokaert & Mayne 1998). Many

distributed methods proposed in the literature (e.g. Du et al., (2001), (Kim & Sugie 2005),

(Dunbar & Murray 2006), (Alessio & Bemporad 2007), (Richards & How 2007), (Venkat et al.,

2008) do not consider the implications that the scheduling of local optimisations has on the time

required for communications. For example, the constraint-tightening DMPC approach proposed

by (Richards & How, 2007), also for dynamically decoupled systems with coupled constraints,

assumes repeated instantaneous exchanges during each sampling period.

2.4 Multi-Agents systems (MAS)

There are several ways to define an agent. Despite all the definitions, the most common view

describes agents like been a high-level software abstraction, which efficiently describes a

complex software entity, or, intelligent entities with three main characteristics:

Pro-Activeness (they react to external events and they are driven to their objectives);

Social ability (they can cooperate or compete between them);

Autonomy (they can decide in order to archive their objectives);

Multi-agent systems can be seen as a group of distributed, autonomous and intelligent

agents within an environment, where they can act and react in order to work together to

achieve a global goal.

Large interconnected networks can hardly be controlled in a traditional way due to its

distributed characteristics and considerable control capabilities over the network operation.

Multi-agent systems have characteristics that meet these requirements, they are able to model

complex systems introducing the possibility of agents having common or conflicting goals.

They may decide cooperating for mutual benefit or may compete to serve their own interests

(Xu et al., 2010). Thus, from the single agent concept to the group of agent’s concept, MAS are

LITERATURE REVIEW

45

a powerful means to represent systems in a natural way. A system is traditionally defined as a

group of components interacting together to achieve an overall objective or a number of

objectives known as the system level objective(s). Each component in a system can be seen as

an agent if it possesses the characteristic of agency, i.e. if it performs computations and its

action is being feedback into the environment (Abbass et al., 2011). Distributed infrastructures

are interconnected and maintain communication between each other is suitable for MAS

technology (Raza et al., 2005) due the follow characteristics:

Agents assess situation on the basis of measurements from sensing devices or that

received from other entities;

Agents cast their influence on performance of networks via commands to actuators and

other identities;

The agents differ in complexity from trivial threshold detectors that merely decide

based upon a single measurement to highly intelligent systems;

Agents have to make real time decisions from local, rather than global state

information;

Agents including controllers for individual devices are designed with simple decision

rules based upon response thresholds that are expected to give most appropriate

responses to a collection of situations generated.

Smart grids can be seen as an environment where a set of simple entities called agents can play

the role of source, load, or any other component integrated in the environment. With the agents

interaction, some collective intelligent can be achieved, they cooperate or compete in other to

reach their objective.

MAS architectures have also others advantages, they are not dependent on a particular

technology, with proper messaging tools, different programming languages can be used and

interact together (Roche et al., 2010), and, due the agents autonomy, they can leave or enter in

the environment without any perturbation.

2.4.1 MAS architectures

Researchers are still attempting to categorize the different types of MAS and agents within

MAS. They are trying to identify characteristics and features that an agent must possess and also

by defining categories of agents and MAS. In (Ferber, 1999) is presented a number of

categorizations of MAS and one of the most accepted formal definitions of as: MAS= {E, O, A,

R, Or, Op} where:

LITERATURE REVIEW

46

E is the environment, a space in which objects (including objects O and agents A) are

located;

O is a set of objects in the environment other than the agents;

A is the set of agents in the environment;

R is an assembly of relations;

Or is an assembly of operators; and,

Op is an assembly of operations.

Due to the flexibility of MAS, several control architectures can be also found in order to

respond to the variety of power systems, such as, voltage control, microgrid management,

distributed network control and restoration, to manage and obtain the desire degree of

intelligence. However, some general types of control structures can be identified and they are

commonly encountered in theory and practice, single-agent, multi-agent single-layer and multi-

layer. A single-agent control structure,

Figure 2.15 occurs when it is assumed that there is only one control agent that has access to all

actuators and sensors of the network and thus directly controls the physical network. This

control structure is referred to as an ideal, since in principle such a control structure can

determine actions that give optimal performance.

Control Agent

Measurements Actions

Control structure

Figure 2.15. Single-agent control structure. (Adapted from Negenborn 2007).

When there are multiple control agents, each of them considering only its own part of the

network and being able to access only sensors and actuators in that particular part of the

network, then the control structure is referred to as a multi-agent single-layer control structure,

Figure 2.16. If in addition the agents in the control structure do not communicate with each

other, the control structure is decentralized. If the agents do communicate with each other (dot

line), the control structure is distributed.

LITERATURE REVIEW

47

Control Agent 1


Control Agent 3

Actions Measurements

Control Agent 2


Control structure

Figure 2.16. Multi-agent single layer control structure. (Adapted from Negenborn 2007).

A multi-layer control structure can be defined when there are multiple control agents and some

of these control agents have authority over other control agents, in the sense that they can force

or direct other control agents,

Figure 2.17. A multi-layer control structure typically is present when one control agent

determines set-points to a group of other control agents working in a decentralized or distributed

way. Due to the authority relationship between agents or groups of agents, this structure can

also be referred to as a supervisory control structure, or a hierarchical control structure.

Control Agent 1


Control Agent 3

Actions Measurements

Control Agent 2


Control Agent 4

Control structure

ActionsMeasurements

Figure 2.17. Multi-layer control structure. (Adapted from Negenborn 2007).

Single-agent control structures in general, have the advantage of deliver the best performance

possible, and that they have been studied extensively in the literature, in particular for small-

scale systems. Although, in large scale systems, there are several issues related with, robustness,

reliability, scalability, responsiveness and communication delays that complicate the use of this

structure.

Multi-agent control structures can deal or at least reduce these issues, but typically, they have a

lower performance comparatively with single-agent.

Decentralized multi-agent single-layer control structures have the advantage, over the

distributed, of lower computational requirements and faster control, because the inexistence of

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48

communication between the controllers. However, this advantage will typically be at the price

of decreased overall performance. The advantage of a distributed multi-agent single layer

control structure is therefore that improved performance can be obtained, although at the price

of increased computation time due to cooperation, communication, and perhaps negotiation

among control agents. The multi-agent multi-layer control structure, despite of been more

complex, provides the possibility to obtain a trade-off between system performance and

computational complexity (Negenborn 2007).

Although all the existing diversity, to respond to the several challenges mentioned above, most

of the authors use a hierarchical layered structure (Zeng et al., 2009; Dimeas et al., 2005; Li et

al., 2010; Aung et al., 2008) to archive different objectives.

With the joint goal of achieving cost and energy savings Ab et al., (1996), shows how

decentralized power load management at the customer side, automatically carried out by a

‘society’ of intelligent household, industrial and utility equipment, can be modelled in terms of

independent hierarchical decentralized intelligent agents that communicate and negotiate in a

computational market economy.

Lu & Chen (2009) proposes new a system-level scheme, a three layered MAS architecture,

where the bottom layer is called physical layer, in which each agent correspond to one energy

source (RE or traditionally), the middle layer is named application layer, which is composed of

coordinator agent, fault diagnosis agent, and recover agent etc., which provides service to the

physical layer. The top layer is the user interface layer, which enables the interaction between

human and MAS.

Also with a hierarchical layered structure, the MAS main target present by Jian et al., (2009), is

to maximize the efficiency of renewable energy resources.

Pipattanasomporn et al., (2009), describes the design and implementation of the multi-agent

system for use in a microgrid. The proposed multi-agent system consists of a control agent, a

DER agent and a user agent in multi-layer distributed architecture where all agents interact

between them. The proposed design also includes a database agent that is responsible for storing

system information, as well as recording the messages and data shared among agents.

In order to negotiate available energy quantities and needs on behalf of consumers and producer

groups, Wedde et al., (2006 and 2008) developed a multi-level bottom-up solution with

autonomous software agents.

Negenborn, (2007), develop a multi-agent control structure with applications to control

problems in power networks, and compare the obtained results with the single-agent approach.

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49

As showed, to respond to the several issues related with distributed nature of the future smart

grids, the MAS structure demonstrate to be the best solution. The existent MAS designs mostly

use layered and subsystems models were a group of agents is controlled by a superior control

agent. However, large distributed systems may have innumerable identities, and due the

necessary communication between agents, it is needed a high computational effort. Besides this

fact, the increase of agents also increases the possibility of internal and external conflicts,

leading to a possible performance reduction.

In order to solve these problems, it is necessary to develop new algorithms, control system

designs, and MAS architectures that can provide the benefits of cooperation, communication

and negotiation among control agents to increase the performance, but with lowest

computational efforts, and also to reduce the complexities to obtain an optimal operation in a

large-scale distributed environment.

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50

51

Chapter 3

3 Dynamical Models and Scenarios

Description

3.1 Introduction

The energy consumption optimization in future SGs will be based on grid-integrated near-real-

time communications between various grid elements in generation, transmission, distribution

and loads.

Figure 3.1. Typical smart grid architecture.

SELECTION AND IDENTIFICATION SCENARIOS AND MODELS

52

Figure 3.1 shows a typical smart metering architecture that is being reflected in the European

standards development process (Fan et al., 2013).

Smart Grid is a concept for transforming the electric power grid using advanced automatic

control and communications techniques and other forms of information technology. It integrates

innovative tools and technologies from generation, transmission and distribution all the way to

consumer appliances and equipment. This concept integrates energy infrastructure, processes,

devices, information and markets into a coordinated and collaborative process that allows

energy to be generated, distributed and consumed more effectively and efficiently. Costumers

will have the chance to decrease their electricity bills by changing consumption from higher-

priced hours to lower priced hours and smart metering will produce a market for new SG

costumer products.

Thus, the scenario here described intends to be a realistic solution to take advantage of these

SG’s features.

3.2 Scenarios overview

A SG generally involves the application of smart meters, sometimes called advanced metering

infrastructure (AMI), which usually include control and monitoring devices and appliances.

Smart metering technology will be at the foundation of any SG design (Cecati et al., 2010). The

most viable communication’s technologies for the AMI are wireless and power line

communication (PLC). SG’s communication’s infrastructure will also provide IP/Ethernet

connectivity between most components, guiding the communication’s interfaces and products

towards TCP/IP-based networks. Power distribution companies are mostly interested in PLC

because it represents the most cost effective solution and does not require additional investment

in the communication’s infrastructure. For these communication’s requirements, companies like

Siemens are offering customized communications network solutions for optic fibre, power line,

and wireless infrastructures based on the accepted standards of the energy industry, Figure 3.2.

Figure 3.2. Typical energy distribution communication architecture for smart grids (Adapted

from Siemens, 2014).


53

Because renewable energies are nowadays significantly expanded, electricity is being fed into

both the medium- voltage and low-voltage grids, depending on changing external conditions

(e.g., weather, time of day, etc.). These fluctuating energy resources can severely impair the

stability of the distribution grid. One of the key challenges of a smart grid is therefore to quick

balance out the energy supply and energy consumption in the distribution grid.

Thus, the scenario here presented has in consideration this challenge, intend to provide a

solution to it based on, and taking advantage of all the AMI and communication technologies

that SG provide.

The conceptual scenario involves a set of buildings with an electricity source provided by their

own renewable energy park and energy storage as presented in Figure 3.3. Henceforward, the

term house will be applied to classify any type of structure for habitation (houses), office

buildings or other kind of analogous constructions. The set 𝑊 = {𝑤1, 𝑤2, … , 𝑤𝑁𝑆} defines the

Thermal Control Areas TCA’s/house and the different spaces are described by 𝐷ℎ =

{𝑑h1, 𝑑h2, … , 𝑑ℎ𝑁𝑑} and h = 1,…𝑁𝑆 .

Figure 3.3. Implemented scheme.

Due the existing division diversity in houses, each area may vary in: construction materials, sun

exposure, occupancy, indoor temperature set-points. This variety involves many different

energy needs to weatherize the spaces, and for this a TCA is considered. Figure 3.4 presents a

conceptual TCA smart thermostat which can be used as an interface for DSM. In the left side of

the display the user is able to choose between three operating modes related with the control

features. At the centre the user is able to program the division’s comfort range and the particular

time periods. On the right the cost, the green and red consumption are shown, allowing the user

to access more specific other menus.


54

Figure 3.4. Thermal Control Area (TCA) smart thermostat controller vision.

Each division may have different thermal loads, thermal characteristics, occupancy and comfort

temperature bounds and consequent different energy needs for heating/cooling the spaces, for

this a Thermal Control Area (TCA) is considered. As mentioned, one TCA represents an

autonomous thermal control entity within an environment where the actions and reactions are

made in order to achieve a common goal. Therefore, as Figure 3.5 shows, depending from the

desired infrastructure intent to be implemented, a set of buildings or a simple division may

represent a TCA.

Figure 3.5. Thermal Control Area concept.

The idea is to use a MPC control law to adjust the indoor temperature set-point in each TCA.

Taking advantage of the MPC characteristics, the system receives information on the outdoor’s

temperature forecasts, the future occupation, the indoor temperature frame and the thermal

disturbances profile. The control action is conditioned by two constraints; thermal comfort and

available energy. Using a DSM approach, the trade-off between the energy price and comfort

limitations are system assured. The scenario considers the existence of two resources, the red,

from the grid provided by fossil source and the green, from renewable or clean source. The first

TEMP. MAX:

TEMP. MIN:

ECO MODE

COMFORT

NORMAL21º

19º

SET TIME PERIOD

13 15-

13:30

SETTINGS

COST

2.5

COMSUNPTION

2.5 KWH

GREEN

0.7RED

78%

22%

INDOOR TEMP.

20º €


55

is always available with a kWh price always higher than the green. On the contrary the green is

limited, intermittent and must be consumed, stored or grid delivered. Remark that if the clean

source becomes insufficient the fossil is consumed increasing the energy costs.

So, the scenario considers that the traded electricity comes from a wholesale market which is

priced in real time, where the market operators (MO) provide the green resource auction and the

agents/TCA set a day-ahead their bids. The agents (one by each TCA) must bid in an auction,

the price that they are willing to pay to consume the green resource. The bid value establishes a

sequential order by which the TCA’s can access to green energy. After consuming, each TCA

sends to the next the information about how much of clean resource is still available. As

mentioned, when the green resource becomes insufficient to satisfy all the demand, the red is

available. The red resource consumption implies a penalty in the final cost function (5.1) due to

the soft constraint violation imposed by the maximum available green resource. Notice that the

divisions that interact thermally pass to each other information about future temperatures.

Each TCA receives several external inputs; the outdoor temperature, available renewable power

forecasts, the MO kWh price, access order to the renewable resource and, when applied, the

neighbour’s indoor temperature forecasts. Figure 3.6 presents an example of the implemented

TCA framework..

Figure 3.6. Example of a TCA conceptual framework.

The example depicted in Figure 3.6 shows the implemented system dependent from weather and

power forecasts. Being wind and solar power not dispatched the production levels need to be

predictable. Lower prediction errors help to balance the supply of wind energy with other

sources, avoid consequences for incorrect estimation, as well as reducing the risk of having to

buy energy from elsewhere. For wind power, the 24 hours ahead prediction average absolute

error can be between 10–20% of installed capacity for one single zone. When aggregation of

Market Operator/

Energy Supplier

Wheather

Forecasts

Available Renewable

Power Forecasts

Neighbors indoor

temperature forecast


56

zones is made, the value may drop to 5-8% (VTT Technology 95, 2014; NREL, 2014). This can

be partly due to the different accuracy for different types of sites, like different orography and

roughness and how homogenous the grid cell for the numerical weather prediction model is.

Prediction errors in low wind situations can still be higher relative to yearly energy. The forecast

error is significantly lowered for the first six hours. The physical reason behind this is that wind

itself has an auto-correlated nature and the model takes this into account by last measured power

value when making forecasts into the future. As the forecast horizon increases the variation

range seems to increase quite linearly.

The forecasting of solar energy production faces issues similar to those of wind. However, solar

forecasting has significant predictability because the sun’s path through the sky is known.

Accurate outdoor temperature forecasts are particularly valuable for electric or gas utilities.

Nowadays, temperature forecasts are particularly reliable and accurate, with more than 92%

accuracy with one day ahead (ForecastWacth, 2014).

Thus, in a scenario that privileges the renewable energy usage, the used demand side

management approach allows the management of distributed loads, aiming the adjustment of the

demand to the supply, providing thermal comfort, lower energy costs and lowering

CO2.emissons. By using this active DSM control, the optimal control strategies for various

appliances can be generated whilst maximum utilisation of energy supplied from intermittent

systems is guaranteed. The used DSM strategy is described in Chapter 3.3.

3.3 Demand side management approach

It is widely accepted that some form of real-time pricing arrangements is required to efficiently

allocate DSM resources and fully inform users about the value of electricity at each point in

time and location. Combination of ICT and business processes will be significant tools in the

real time management of active networks, customers and commercial systems. Deregulated

markets will let consumers to exploit information to move between competing energy suppliers

based on energy cost, greenhouse gas emissions and social goals. A SG vision for the market

has been developed in recent years through the work of a consortium of utilities. One option is

an “eBay for electricity”, where continual electronic sales match energy consumers with energy

producers. Soon customers will be able to bond the electricity pricing into their energy

management system. High gap in price differentials between cost periods could result in greater

shifts of energy usage. This needs to be accompanied by the application of intelligent appliances

that would facilitate the implementation of DSM. In order to simplify such trading of energy

among a very large number of smaller domestic participants, an electronic energy market


57

system, supported for example by the internet, would need to be developed (an extension of

power-exchange-type markets).

Thus, the developed system intends to provide a solution to be implemented in these future

energy markets. It considers that the MO offers a green resource auction where each TCA sets a

day-ahead their bids. The agents (one by each TCA) must bid in an auction, the price that they

are willing to pay to consume the green resource according to their own consumption forecasts.

Utilities are able to see what power loads are creating bigger demand on their side, allowing

them to more effectively implement DR programs for heating and cooling. Although, before

demand–response systems can be effectively deployed on a wide scale in the residential sector,

a number of technical challenges need to be resolved (infrastructure of communications,

metering infrastructure, demand–response thermostats, etc.). This is likely to include some form

of house energy management system that may rely on wireless technology that would

automatically respond to price signals while taking into consideration the homeowner's

preferences for cost versus comfort. Furthermore, the thermostat can be programmed to change

settings with seasons. The thermostats can also have a notification feature to alert residents for

calls for action, as well as an override feature, in case the customer chooses not to participate in

the particular event. The customer main obtain information on buy-back rates via internet

connections and takes appropriate action to manage peak loads. A key issue in these

programmes is how sophisticated or complex they need to be to make the price signals. There is

also the issue of verification to confirm that some benefit was obtained when the thermostat and

air-conditioning system responded. Thermostats can also be pre-programmed to receive weather

forecasts, to optimize both a consumer's energy savings and grid performance. The system uses

weather forecasts and, when applied, neighbours indoor temperature forecasts, to anticipate

major changes in the surrounding temperature and manage heating and cooling needs in

advance, in the most energy-efficient way.

3.4 TCA Dynamical Models

The dynamics of temperature evolution in a building is one of the most important aspects of the

overall building dynamics. The complexity in the dynamics of temperature evolution comes

from the thermal interaction among rooms (and the outside). This interaction can either be

through conduction across the walls, or through convective air exchanging among rooms.

Consumption of energy is predominantly determined from a selection of materials and

architectural solutions. It can be further reduced with efficient management of heating or

cooling.


58

The building geometry constitutes the basic input for energy simulation. It is crucial to

understand the differences between a building model created by an architect and a building

model needed for energy simulation. For example, energy simulations spaces need to be defined

by space boundaries, which are not necessarily the same as walls in an architectural model.

Thermal building simulation engines like, EnergyPlus or DOE-2 (Maile et al., 2007), predict the

energy performance of a given building and thermal comfort for its occupants. In general, they

support the understanding of how a given building operates according to certain criteria and

enable comparisons of different design alternatives. This kind of software allows designing and

characterizing in detail all the major features of a building architecture. Most of them also

require a set of inputs which mainly consist in building geometry, internal loads, HVAC

systems and components, weather data, operating strategies and schedules and simulation of

specific parameters. However, these tools are only used for thermal simulation with predicted

scenarios and previously established data, not working with real time inputs and data, which

allow instant action over devices with control and decision mechanisms.

Figure 3.7. Energy modelling and building design process example with EnergyPlus.

Every energy simulation is based on thermodynamic equations, principles and assumptions.

Since thermal processes in buildings are today complex and not totally understood, energy

simulation programs estimate their predictions with qualified equations and methods. Therefore,

results can be arbitrarily incorrect, if certain assumptions are not satisfied or matched in the

simulation in real life. While two or three dimensional heat transfer would increase the accuracy

of simulation results, geometry input and simulation running at real time is likely to become

more complex. As mentioned earlier, the input, especially weather data and internal loads, for

energy simulation is already based on assumptions, as are the thermodynamic concepts. For that


59

matter, any simulation is based on assumptions; therefore complex interrelations can be

simplified and managed. Users need to be aware of these assumptions and be able to decide

whether they are reasonable for their specific simulation or not. Thus, the idea here presented is

to apply the principle of analogy between two different physical domains that can be described

by the same mathematical equations. Consequently, a linear electrical circuit represents the

building, the state-space equations are obtained by solving the circuit. Here, the temperature is

equivalent to voltage and the heat flux to current. Heat transmission resistance is represented by

electrical resistance and thermal capacity by electrical capacity. The building equivalent circuit

is obtained by assembling models of the walls, windows, internal mass, etc. For single-zone

buildings, interior walls are part of the internal thermal mass, while exterior walls form the

building envelope. Several approaches are seen in (Zong et al., 2012; Hazyuk et al. 2011) where

is shown that building models can be simple or more complex depending on the objective.

Therefore, the first order energy balance model (3.1)-(3.3) that describes the dominant dynamics

of a generic division, is considered suitable for control purposes (Barata et al., 2014b). Note that

these are basic equations for edifice thermal modelling which can be described by several

divisions and floors thermally interacting between them. For complete thermal models see

(Hazyuk et al. 2011).

𝑑𝑇𝑙𝑖

𝑑𝑡=

1

𝐶𝑙𝑒𝑞𝑖(𝑄𝑙

𝑖ℎ𝑒𝑎𝑡

− 𝑄𝑙𝑙𝑜𝑠𝑠𝑒𝑠𝑖 + 𝑄𝑙𝑃𝑑

𝑖 ), (3.1)

𝑄𝑙𝑙𝑜𝑠𝑠𝑒𝑠𝑖 =

𝑇𝑜𝑢𝑡 − 𝑇𝑙𝑖

𝑅𝑙𝑒𝑞𝑖

+ ∑𝑇𝑔𝑖 − 𝑇𝑙

𝑖

𝑅𝑙𝑔𝑒𝑞𝑖 𝐶𝑙𝑒𝑞

𝑖𝛥𝑡

𝑁𝑑𝑖

𝑔=1(𝑔≠𝑙)

+ ∑ ∑𝑇𝑚ℎ − 𝑇𝑙

𝑖

𝑅𝑙𝑚𝑒𝑞𝑖ℎ 𝐶𝑙𝑒𝑞

𝑖

𝑁𝑑ℎ

𝑚=1

𝑁𝑠

ℎ=1(ℎ≠𝑖)

, (3.2)

𝑅𝑙𝑒𝑞𝑖 = 𝑅𝑙𝑟𝑜𝑜𝑓

𝑖 //𝑅𝑙𝑤𝑖𝑛𝑑𝑜𝑤𝑠𝑖 //𝑅𝑙𝑤𝑎𝑙𝑙𝑠

𝑖 //𝑅𝑙𝑡ℎ𝑖 , (3.3)

𝑅𝑙𝑤𝑖𝑛𝑑𝑜𝑤𝑠𝑖 =∑𝑅𝑤𝑖𝑛𝑑𝑜𝑤𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙𝑠 , (3.3a)

𝑅𝑙𝑟𝑜𝑜𝑓𝑖 =∑𝑅𝑟𝑜𝑜𝑓𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙𝑠 , (3.3b)

𝑅𝑙𝑤𝑎𝑙𝑙𝑠𝑖 =∑𝑅𝑤𝑎𝑙𝑙𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙𝑠 , (3.3c)

where in (3.1), 𝑄𝑙𝑙𝑜𝑠𝑠𝑒𝑠𝑖 is heat and cooling losses (kW) from division (l), 𝑇𝑙

𝑖 the inside

temperature (ºC), 𝐶𝑙𝑒𝑞𝑖 the equivalent thermal capacitance (kJ/ºC), and 𝑄𝑙

𝑖ℎ𝑒𝑎𝑡

the heat and

cooling power (kW) and 𝑄𝑙𝑃𝑑𝑖 the external thermal disturbances (kW) (e.g. load generated by

occupants, direct sunlight, electrical devices or doors and windows aperture to recycle the


60

indoor air). In (3.2) 𝑇out is the outdoor temperature (ºC), 𝑅𝑙𝑔𝑒𝑞𝑖 the thermal resistance between

division (l) and the adjacent zone (g), 𝑅𝑙𝑒𝑞𝑖 the equivalent thermal resistance (C/kW), and 𝑅𝑙𝑡ℎ

𝑖 the

air thermal resistance to bulk of division.

Figure 3.8 and Figure 3.9 present a simplified schematic representation of thermal-electrical

modular analogy described by (3.1)-(3.3). 𝑇1𝑖…𝑇𝑁𝑑𝑖

𝑖 are the inside temperature of adjacent

spaces inside the same house, and 𝑅1𝑖 …𝑅𝑁𝑑𝑖

𝑖 the equivalent thermal resistance between the

division and that adjacent areas.

Figure 3.8. Schematic representation of thermal-electrical modular analogy for one division.

Figure 3.9. Generic schematic representation of thermal-electrical modular analogy for several

divisions (Barata et al., 2014b).

Tout

...

Ceq

Req

heat

i

l Qu

i

l

i

l Tx

...

Pd

i

l Qv

ii xT 11

i

Nd

i

Nd iixT

iR1

i

Nd iR

Thermal interconnections

with division of neighboring

houses

... Thermal interconnections

within the same house

T1Tout

Qheat1 Qlosses1C1

Req1

T2Tout

Qheat2 Qlosses2C2

Req2

TnTout

Qheatn QlossesnCn

Reqn

R2n

R12

R1n

...

...

T2, C2, Qheat2,

Req2, , QPd2

Tout

T3, C3, Qheat3,

Req3, QPd3

T1, C1,

Qheat1, Req1

QPd1


61

As described in (Barata, et al., 2013b), a first order energy balance model is used to define the

dominant dynamics of a generic division. Remark that these are the basic equations for structure

thermal modelling and can be described by several divisions and floors interacting between

them. In literature there are several degrees of complexity for house modelling techniques

(Thavlov, 2008). The model used is linear and considers control purposes suitability,

𝒙(𝑘 + 1) = 𝑨𝒙(𝑘) + 𝑩𝒖(𝑘) + 𝒗(𝑘), (3.4)

where x ℝn is the state variable, indoor temperatures, vector containing all the divisions

temperatures (ºC), u ℝm is the input vector containing all the heating and cooling power

sources (W) to weatherize each division, and v ℝn includes all the disturbances (W),

including load generated by occupants, solar radiation, any other heat/cooling sources or doors

and windows aperture to recycle the indoor air, k is an integer number that denotes discrete time

and A ℝn×n, B ℝn×m, are matrices.

Generically, using Euler discretization (Bequette, 2003) with a sampling time of , the discrete

model space-state representation of (3.4) can be written, for the Ns TCAs and for each division

(l) as,

𝑇𝑙𝑖(𝑘 + 1) = 𝐴𝑙𝑙

𝑖𝑖𝑇𝑙𝑖(𝑘) + 𝐵𝑙

𝑖𝑢𝑙𝑖(𝑘) + ∑ (𝐴𝑙𝑔

𝑖𝑖 𝑇𝑔𝑖(𝑘))

𝑁𝑑𝑖

𝑔=1(𝑔≠𝑙)⏟

𝑡ℎ𝑒𝑟𝑚𝑎𝑙 𝑐𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛𝑠 𝑓𝑟𝑜𝑚 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑎𝑟𝑒𝑎𝑠 𝑖𝑛𝑠𝑖𝑑𝑒 𝑡ℎ𝑒 𝑠𝑎𝑚𝑒 ℎ𝑜𝑢𝑠𝑒

+ ∑ ∑ (𝐴𝑙𝑚𝑖ℎ 𝑇𝑚

ℎ(𝑘))

𝑁𝑑ℎ

𝑚=1

𝑁𝑠

ℎ=1(ℎ≠𝑖)⏟ 𝑡ℎ𝑒𝑟𝑚𝑎𝑙 𝑐𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛𝑠 𝑓𝑟𝑜𝑚 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑎𝑟𝑒𝑎𝑠 𝑓𝑟𝑜𝑚 𝑜𝑡ℎ𝑒𝑟 ℎ𝑜𝑢𝑠𝑒𝑠

+ 𝑣𝑙𝑖(𝑘),

(3.5)

where

𝐴𝑙𝑙𝑖𝑖 = (1 −

𝛥𝑡

𝑅𝑙𝑒𝑞𝑖 𝐶𝑙𝑒𝑞

𝑖) , 𝐵𝑙

𝑖 =𝛥𝑡

𝐶𝑙𝑒𝑞𝑖, 𝐷𝑙

𝑖 = ∑𝑇𝑔𝑖 − 𝑇𝑙

𝑖

𝑅𝑙𝑔𝑒𝑞𝑖 𝐶𝑙𝑒𝑞

𝑖𝛥𝑡

𝑁𝑑𝑖

𝑔=1(𝑔≠𝑙)

+ ∑ ∑𝑇𝑚ℎ − 𝑇𝑙

𝑖

𝑅𝑙𝑚𝑒𝑞𝑖 𝐶𝑙𝑒𝑞

𝑖𝛥𝑡

𝑁𝑑ℎ

𝑚=1

𝑁𝑠

ℎ=1(ℎ≠𝑖)

,

𝑣𝑙𝑖 =

𝑃𝑙𝑃𝑑𝑖 𝛥𝑡

𝐶𝑙𝑒𝑞𝑖

+𝑇𝑜𝑎𝛥𝑡


𝑖.

(3.6)

where Ns is number of TCA’s, Ndi is number of divisions inside subsystem (i), 𝑥𝑙𝑖 is the indoor

temperature in TCA/subsystem (i) inside division (l), 𝑢𝑙𝑖 is the used power to provide comfort in

TCA/subsystem (i) inside division (l), 𝐴𝑙𝑚𝑖ℎ is an element from the state matrix A that relates the

state (indoor temperature) in division (m) from TCA/subsystem (h), with the state from division

(l) in TCA (i) and 𝑣𝑙𝑖 is the thermal disturbance in TCA/subsystem (i) inside division (l) e(g.

load generated by occupants, direct sunlight, electrical devices or doors and windows aperture

to recycle the indoor air), and Toa, the temperature of outside air (ºC). Remark that the number

of states variables in general model (3.4) is


62

𝑛 =∑ 𝑁𝑑𝑖𝑁𝑠

𝑖=1.

To exemplify, Figure 3.10 illustrates a house/TCA with six divisions that thermally interact

between them.

Figure 3.10. TCA divisions interaction simplified scheme;

So, for each division, (3.4) can be written as:

𝑥11(𝑘 + 1) = 𝐴11

11𝑥11(𝑘) + 𝐴12

11𝑥21(𝑘) + 𝐵1

1𝑢11(𝑘) + 𝑣1

1(𝑘),

𝑥21(𝑘 + 1) = 𝐴22

11𝑥21(𝑘) + 𝐴21

11𝑥11(𝑘) + 𝐴23

11𝑥31(𝑘) + 𝐴24

11𝑥41(𝑘) + 𝐴26

11𝑥61(𝑘) + 𝐵2

1𝑢21(𝑘) + 𝑣2

1(𝑘),

𝑥31(𝑘 + 1) = 𝐴33

11𝑥31(𝑘) + 𝐴32

11𝑥21(𝑘) + 𝐴35

11𝑥51(𝑘) + 𝐴36

11𝑥61(𝑘) + 𝐵3

1𝑢31(𝑘) + 𝑣3

1(𝑘), (3.7)

𝑥41(𝑘 + 1) = 𝐴44

11𝑥41(𝑘) + 𝐴42

11𝑥21(𝑘) + 𝐴45

11𝑥51(𝑘) + 𝐴46

11𝑥61(𝑘) + 𝐵4

1𝑢41(𝑘) + 𝑣4

1(𝑘),

𝑥51(𝑘 + 1) = 𝐴55

11𝑥51(𝑘) + 𝐴53

11𝑥31(𝑘) + 𝐴54

11𝑥41(𝑘) + 𝐴56

11𝑥61(𝑘) + 𝐵5

1𝑢51(𝑘) + 𝑣5

1(𝑘),

𝑥61(𝑘 + 1) = 𝐴66

11𝑥61(𝑘) + 𝐴62

11𝑥21(𝑘) + 𝐴63

11𝑥31(𝑘) + 𝐴64

11𝑥41(𝑘) + 𝐴65

11𝑥51(𝑘) + 𝐵6

1𝑢61(𝑘) + 𝑣6

1(𝑘),

dl1 dl2

dl4 dl3

dl5

dl6


63

[ 𝑥11(𝑘 + 1)

𝑥21(𝑘 + 1)

𝑥31(𝑘 + 1)

𝑥41(𝑘 + 1)

𝑥51(𝑘 + 1)

𝑥61(𝑘 + 1)]

=

[ 𝐴1111 0 0 0 0 0

0 𝐴2211 0 0 0 0

0 0 𝐴3311 0 0 0

0 0 0 𝐴4411 0 0

0 0 0 0 𝐴5511 0

0 0 0 0 0 𝐴6611]

[ 𝑥11(𝑘)

𝑥21(𝑘)

𝑥31(𝑘)

𝑥41(𝑘)

𝑥51(𝑘)

𝑥61(𝑘)]

+

[ 0 𝐴12

11 0 0 0 0

𝐴2111 0 𝐴23

11 𝐴2411 0 𝐴26

11

0 𝐴3211 0 0 𝐴35

11 𝐴3611

0 𝐴4211 0 0 𝐴45

11 𝐴4611

0 0 𝐴5311 𝐴54

11 0 𝐴5611

0 𝐴6211 𝐴63

11 𝐴6411 𝐴65

11 0 ]

[ 𝑥11(𝑘)

𝑥21(𝑘)

𝑥31(𝑘)

𝑥41(𝑘)

𝑥51(𝑘)

𝑥61(𝑘)]

+

[ 𝐵11 0 0 0 0 0

0 𝐵21 0 0 0 0

0 0 𝐵31 0 0 0

0 0 0 𝐵41 0 0

0 0 0 0 𝐵51 0

0 0 0 0 0 𝐵61]

[ 𝑢11(𝑘)

𝑢21(𝑘)

𝑢31(𝑘)

𝑢41(𝑘)

𝑢51(𝑘)

𝑢61(𝑘)]

+

[ 𝑣11(𝑘)

𝑣21(𝑘)

𝑣31(𝑘)

𝑣41(𝑘)

𝑣51(𝑘)

𝑣61(𝑘)]

.

(3.8)

For a more complex scenario, Figure 3.11 shows a distributed environment with five houses

with different plans and with different zones that may thermally interact. Remark that as

described in the sequel, adjacent areas can be doubly coupled, thermally and by the power

constraint. In Figure 3.11, ui represents the input (heat/cooling power) and yi is the output vector

containing the temperatures/states inside the several divisions of house (i)

Figure 3.11. Generalized house/TCA scheme example.

Thus, (3.4) can be generalized and presented as:

𝑥11(𝑘 + 1) = 𝐴11

11𝑥11(𝑘) + 𝐴12

11𝑥21(𝑘) + 𝐴13

11𝑥31(𝑘) + 𝐴11

12𝑥12(𝑘)+𝐴12

12𝑥22(𝑘)+𝐵1

1𝑢11(𝑘) + 𝑣1

1(𝑘),

𝑥21(𝑘 + 1) = 𝐴22

11𝑥21(𝑘) + 𝐴21

11𝑥11(𝑘) + 𝐴23

11𝑥31(𝑘)+𝐵2

1𝑢21(𝑘) + 𝑣(𝑘),

𝑥31(𝑘 + 1) = 𝐴33

11𝑥31(𝑘) + 𝐴32

11𝑥21(𝑘) + 𝐴31

11𝑥11(𝑘) + 𝐴32

12𝑥22(𝑘)+𝐵3

1𝑢31(𝑘) + 𝑣3

1(𝑘),

𝑥12(𝑘 + 1) = 𝐴11

22𝑥12(𝑘) + 𝐴12

22𝑥22(𝑘) + 𝐴11

21𝑥11(𝑘)+𝐵1

2𝑢12(𝑘) + 𝑣1

2(𝑘),

𝑥22(𝑘 + 1) = 𝐴22

22𝑥22(𝑘) + 𝐴21

22𝑥12(𝑘) + 𝐴21

21𝑥11(𝑘) +

𝐴2321𝑥3

1(𝑘)+𝐴2223𝑥2

3(𝑘) + 𝐴2124𝑥1

4(𝑘) + 𝐵22𝑢2

2(𝑘) + 𝑣22(𝑘),

(3.9)

1

2

43

1u

1y

2u

2y

3u

3y4u

4y

55u

5yd11

d12

d13

d22d31

d32

d41

d21w3

w2

w1

w4d51

w5


64

𝑥13(𝑘 + 1) = 𝐴11

33𝑥13(𝑘) + 𝐴12

33𝑥23(𝑘) + 𝐴11

34𝑥14(𝑘)+𝐵1

3𝑢13(𝑘) + 𝑣1

3(𝑘),

𝑥23(𝑘 + 1) = 𝐴22

33𝑥23(𝑘) + 𝐴21

33𝑥13(𝑘) + 𝐴21

34𝑥14(𝑘)𝐴21

32𝑥12(𝑘)+𝐴22

32𝑥22(𝑘) + 𝐵2

3𝑢23(𝑘) + 𝑣2

3(𝑘),

𝑥14(𝑘 + 1) = 𝐴11

44𝑥14(𝑘) + 𝐴11

43𝑥13(𝑘) + 𝐴12

43𝑥23(𝑘)𝐴12

42𝑥22(𝑘) + 𝐵1

4𝑢14(𝑘) + 𝑣1

4(𝑘),

𝑥15(𝑘 + 1) = 𝐴11

55𝑥15(𝑘)+𝐵1

5𝑢15(𝑘) + 𝑣1

5(𝑘),

[ 𝑥11(𝑘 + 1)

𝑥21(𝑘 + 1)

𝑥31(𝑘 + 1)

𝑥12(𝑘 + 1)

𝑥22(𝑘 + 1)

𝑥13(𝑘 + 1)

𝑥23(𝑘 + 1)

𝑥14(𝑘 + 1)

𝑥15(𝑘 + 1)]

=

[ 𝐴1111 𝐴12

11 𝐴1311 𝐴11

12 𝐴1212 0 0 0 0

𝐴2111 𝐴22

11 𝐴2311 0 0 0 0 0 0

𝐴3111 𝐴31

11 𝐴3311 𝐴32

12 0 0 0 0 0

𝐴1121 0 0 𝐴11

22 𝐴1222 0 0 0 0

𝐴2121 0 𝐴23

21 𝐴2121 𝐴22

22 0 𝐴2223 𝐴21

24 0

0 0 0 0 0 𝐴1133 𝐴12

33 𝐴1134 0

0 0 0 𝐴2132 𝐴22

32 𝐴2133 𝐴22

33 𝐴2134 0

0 0 0 𝐴1242 0 𝐴11

43 𝐴1243 𝐴11

44 0

0 0 0 0 0 0 0 0 𝐴1155]

[ 𝑥11(𝑘)

𝑥21(𝑘)

𝑥31(𝑘)

𝑥12(𝑘)

𝑥22(𝑘)

𝑥13(𝑘)

𝑥23(𝑘)

𝑥14(𝑘)

𝑥15(𝑘)]

+

+

[ 𝐵11 0 0 0 0 0 0 0 0

0 𝐵21 0 0 0 0 0 0 0

0 0 𝐵31 0 0 0 0 0 0

0 0 0 𝐵12 0 0 0 0 0

0 0 0 0 𝐵22 0 0 0 0

0 0 0 0 0 𝐵13 0 0 0

0 0 0 0 0 0 𝐵23 0 0

0 0 0 0 0 0 0 𝐵14 0

0 0 0 0 0 0 0 0 𝐵15]

[ 𝑢11(𝑘)

𝑢21(𝑘)

𝑢31(𝑘)

𝑢12(𝑘)

𝑢22(𝑘)

𝑢13(𝑘)

𝑢23(𝑘)

𝑢14(𝑘)

𝑢15(𝑘)]

+

[ 𝑣11(𝑘)

𝑣21(𝑘)

𝑣31(𝑘)

𝑣12(𝑘)

𝑣22(𝑘)

𝑣13(𝑘)

𝑣23(𝑘)

𝑣14(𝑘)

𝑣15(𝑘)]

.

65

Chapter 4

4 MPC and PI control in thermal

comfort systems

4.1 Introduction

The chapter presents the first approach towards the final developed control structure. It allowed

us to understand the problem, its dynamics and to verify that the MPC control strategy is

suitable for the objective that is intent to be achieved. So, it considers one house/TCA and no

communication with neighbouring is taking into account (Barata et al., 2012a).

The methodologies are based on a predictive control structure associated to a PI controller and

applied to the thermal house comfort in an environment with limited energy sources. Thus, the

available and necessary power to cool and heat the house within the desire “comfort zone” is

partially available and, consequently constrained. The system also uses the house thermal inertia

to “accommodate thermal energy” within the selected temperature range, maintaining the

comfort when no energy is available and reducing the energy consumption without loss of the

thermal comfort. The simulation results obtained with traditional PI and with MPC are

presented and it can be seen that the system is able to provide high-energy conservation and

reliable comfort. The house temperature variations are calculated and are taking into account the

necessary heat and cooling needs and heat losses to the environment. The indoor temperature

time derivative is expressed as follows,

𝑑𝑇𝑙𝑖

𝑑𝑡=

1

𝐶𝑙𝑒𝑞𝑖(𝑄𝑙

𝑖ℎ𝑒𝑎𝑡

− 𝑄𝑙𝑙𝑜𝑠𝑠𝑒𝑠𝑖 + 𝑄𝑙𝑃𝑑

𝑖 ). (4.1)

MPC AND PI CONTROL IN THERMAL COMFORT SYSTEMS

66

Actually (4.1) is not an accurate model of the house. Nevertheless, it reflects well enough the

dominant model of a real house to be used for designing the MPC controller.

The heat loss is mainly a function of outdoor air temperature. By taking the outdoor temperature

as a primary influencing factor for the weather, the heat loss is given by,

𝑄𝑙𝑙𝑜𝑠𝑠𝑒𝑠𝑖 =

𝑇𝑜𝑢𝑡 − 𝑇𝑙𝑖

𝑅𝑙𝑒𝑞𝑖

. (4.2)

The parameter 𝑅𝑙𝑒𝑞𝑖 describes the equivalent thermal resistance of all walls (including roof and

ceiling) and windows that isolate the house from outside, and can be describe as a electrical

parallel resistance circuit (Gulley and Chistol, 2006; Ma, et al., 2012).

𝑅𝑙𝑒𝑞𝑖 = 𝑅𝑙𝑤𝑎𝑙𝑙𝑠

𝑖 //𝑅𝑙𝑤𝑖𝑛𝑑𝑜𝑤𝑠𝑖 . (4.3)

As also used in (Löhnberg, 1999; Mendes, et al., 2001), the external temperature disturbance

variation, Tout, can be approximated represented by a sine (with a given amplitude) where is

added a constant temperature value. Other disturbances can be reflected in (4.1), like heat flux

from solar radiation, inside loads generated by occupancy, lights or other electrical devices (Ma,

et al., 2012).

The plant model representation (4.1) can be rewritten and changed into a discrete model.

𝑦(𝑘 + 1) = 𝑎𝑦(𝑘) + 𝑏𝑢(𝑘) + 𝑐𝑣(𝑘), (4.4)

where, 𝑎 = (1 −Δt


𝑖 ) , 𝑏 =Δt

𝐶𝑙𝑒𝑞𝑖 , c=

Δt


𝑖 , u(k) is the necessary heat/cooling power, v(k)

are the disturbances and y(k) is the indoor temperature. Note that the space is cooled when u(k)

< 0 and heated when u(k) > 0.

4.2 System description

As a first approach towards developing a control structures it is considered an individual house,

Figure 4.1. As mentioned, this approach does not take into account the possibility of

communication with neighbouring houses.


67

PI

+

HVACMPC

-+

r0(k) u(k) y(k)

v(k)

Disturbances forecasts

Environment temperature,

solar loadsEnvironment temperature,

solar loads

Disturbances

Avaiable power

Figure 4.1. Block diagram of the implemented system.

The following discrete equations describe the implemented system showed in Figure 4.1.

𝑌(𝑧) =𝑏

𝑧 − 𝑎𝑈(𝑧) +

𝑐

𝑧 − 𝑎𝑉(𝑧). (4.5)

With the controller described by,

𝑃𝐼 = 𝑘𝑝 +𝑘𝑖𝑧

𝑧 − 1=𝑧(𝑘𝑝 + 𝑘𝑖) − 𝑘𝑝

𝑧 − 1. (4.6)

Being

𝑈(𝑧) = 𝑘𝑧 − 𝛽

𝑧 − 1𝐸(𝑧), (4.7)

and

𝐸(𝑧) = 𝑅0(𝑧) − 𝑌(𝑧). (4.8)

Figure 4.1 can also be characterized by the following discrete equations, where (4.9) and (4.10)

describe the system and (4.11) and (4.12) the controller.

𝑥(𝑘 + 1) = 𝐴𝑥(𝑘) + 𝐵𝑢(𝑘) + 𝐸𝑣(𝑘), (4.9)

𝑦(𝑘) = 𝐶𝑥(𝑘), (4.10)

𝜉(𝑘 + 1) = 𝐴𝑐𝜉(𝑘) + 𝐵𝑐[𝑟(𝑘) − 𝑦(𝑘)], (4.11)

𝑢(𝑘) = 𝐶𝑐𝜉(𝑘). (4.12)

Substituting (4.12) in (4.9) and (4.10) in (4.11) results in (4.13) and (4.14), respectively that

describe the close-loop system in u(k).

𝑥(𝑘 + 1) = 𝐴𝑥(𝑘) + 𝐵𝐶𝑐𝜉(𝑘) + 𝐸𝑣(𝑘), (4.13)


68

𝜉(𝑘 + 1) = 𝐴𝑐𝜉(𝑘) + 𝐵𝑐[𝑟(𝑘) − 𝐶𝑥(𝑘)], (4.14)

[𝑥(𝑘 + 1)

𝜉(𝑘 + 1)] = [

𝐴 𝐵𝐶𝑐−𝐵𝑐𝐶 𝐴𝑐

] [𝑥(𝑘)

𝜉(𝑘)] + [

0𝐵𝑐] 𝑟(𝑘) + [

𝐸0] 𝑣(𝑘). (4.15)

The following equations describe the close-loop system ∆r(k)

𝑟(𝑘) = 𝛥𝑟(𝑘) + 𝑟(𝑘 − 1), (4.16)

𝑥(𝑘 + 1) = 𝐴𝑥(𝑘) + 𝐵𝐶𝑐𝜉(𝑘) + 𝐸𝑣(𝑘). (4.17)

Equation (4.18) results from substituting (4.16) in (4.14).

𝜉(𝑘 + 1) = 𝐴𝑐𝜉(𝑘) − 𝐵𝑐𝐶𝑥(𝑘) + 𝐵𝑐[𝛥𝑟(𝑘) − 𝑟(𝑘 − 1)], (4.18)

with

𝛾(𝑘) = 𝑟(𝑘 − 1), (4.19)

𝛾(𝑘 + 1) = 𝛾(𝑘) + 𝛥𝑟(𝑘), (4.20)

𝑥(𝑘 + 1) = 𝐴𝑥(𝑘) + 𝐵𝐶𝑐𝜉(𝑘) + 𝐸𝑣(𝑘). (4.21)

Substituting (4.20) in (4.18) results in

𝜉(𝑘 + 1) = −𝐵𝑐𝐶𝑥(𝑘) + 𝐴𝑐𝜉(𝑘) + 𝐵𝑐𝛾(𝑘) + 𝐵𝑐𝛥𝑟(𝑘), (4.22)

[

𝑥(𝑘 + 1)

𝜉(𝑘 + 1)

𝛾(𝑘 + 1)] = [

𝐴 𝐵𝐶𝑐 0−𝐵𝑐𝐶 𝐴𝑐 𝐵𝐶 0 0 𝐼

]

⏞ 𝐴1

[

𝑥(𝑘)𝜉(𝑘)

𝛾(𝑘)]

⏞ 𝜁(𝑘)

+ [0 𝐸𝐵𝐶 0𝐼 0

]

⏞ [𝐵1 𝐵2]

[𝛥𝑟0(𝑘)𝑣(𝑘)

], (4.23)

𝑦(𝑘) = [𝐶 0 0⏟ 𝐶𝑦

] [

𝑥(𝑘)

𝜉(𝑘)

𝛾(𝑘)], (4.24)

𝑢(𝑘) = [0 𝐶𝑐 0⏟ 𝐶𝑢

] [

𝑥(𝑘)𝜉(𝑘)

𝛾(𝑘)], (4.25)

𝑟 = [0 0 𝐼] [

𝑥(𝑘)

𝜉(𝑘)

𝛾(𝑘)], (4.26)

Or,

𝜉(𝑘 + 1) = 𝐴1𝜁(𝑘) + 𝐵1𝛥𝑟0(𝑘) + 𝐵2𝑣(𝑘), (4.27)


69

𝑦(𝑘) = 𝐶𝑦𝜁(𝑘) 𝑢(𝑘) = 𝐶𝑢𝜁(𝑘). (4.28)

As mentioned in Chapter 2.3 predictive control is based on the receding horizon principle in

which, at each sample interval, the current controller output is obtained by solving an optimal

control problem of finite horizon. The input to the controller is current output/state information

and the output is a sequence of future control actions where usually the first element in the

sequence is applied to the plant.

Predictive control belongs to the class of model-based designs where a model of the plant is

used to predict the behaviour of the plant and calculate the controller output such that a given

control criterion is minimized.

The criterion must be selected such that the performance and robustness specifications are

accomplished. The GPC criterion introduced in (Clarke et al., 1987) is of the form:

𝐽 = ∑[∑‖𝑦𝑖(𝑘 + 𝑙) − 𝑦𝑖𝑑(𝑘 + 𝑙)‖

𝑄𝑖

2+

𝐻𝑃

𝑙=1

∑‖𝛥𝑢𝑖(𝑘 + 𝑙 − 1)‖𝑅𝑖2

𝑁𝐶

𝑙=1

]

𝑛

𝑖=1

, (4.29)

where Qi and Ri are weight matrices, HP, NC are predictive horizon and control horizon,

respectively, and HP ≥ M, yid is the set-point of subsystem Si , Δui(k) = ui(k) − Δui(k − 1) is

the input increment vector of subsystem Si .

Considering Figure 4.1, (4.29) can be rewritten,

𝐽 =∑[∑‖𝑦𝑖(𝑘 + 𝑙) − 𝑟𝑖𝑑(𝑘 + 𝑙)‖

𝑄𝑖

2+

𝐻𝑃

𝑙=1

∑‖𝛥𝑟𝑜𝑖(𝑘 + 𝑙 − 1)‖𝑅𝑖2

𝑁𝐶

𝑙=1

]

𝑛

𝑖=1

. (4.30)

Then the model outputs in future sample intervals are given as follows:

𝑦 = [

𝑦 (𝑘 + 1)

𝑦 (𝑘 + 2)⋮

𝑦 (𝑘 + 𝐻𝑃)

] = [

𝑦 𝑜(𝑘 + 1)

𝑦 𝑜(𝑘 + 2)⋮

𝑦 𝑜(𝑘 + 𝐻𝑃)

] + [

𝑔1 0 … 0𝑔2 𝑔1 ⋱ ⋮⋮ ⋮ ⋱ 0𝑔𝐻𝑃 𝑔𝐻𝑃−1 … 𝑔𝐻𝑃−𝑁𝐶−1

]

× [

∆𝑟𝑜(𝑘)

∆𝑟𝑜(𝑘 + 1)⋮

∆𝑟𝑜(𝑘 + 𝑁𝐶 − 1)

].

(4.31)

Where,


70

[

𝑦 𝑜(𝑘 + 1)

𝑦 𝑜(𝑘 + 2)⋮

𝑦 𝑜(𝑘 + 𝐻𝑃)

] =

[ 𝐶1𝐴1 𝐶2𝐴2 … 𝐶𝑛𝐴𝑛𝐶1𝐴1

2 𝐶2𝐴22 ⋱ 𝐶𝑛𝐴𝑛

2

⋮ ⋮ ⋱ ⋮𝐶1𝐴1

𝐻𝑃 𝐶2𝐴2𝐻𝑃 … 𝐶𝑛𝐴𝑛

𝐻𝑃] [

𝑥𝑜(𝑘)

𝑥𝑜(𝑘 + 1)⋮

𝑥𝑜(𝑘 + 𝑁𝐶 − 1)

] +

[

𝑤1 0 … 0𝑤1 𝑤1 ⋱ ⋮⋮ ⋮ ⋱ 0𝑤𝐻𝑃 𝑤𝐻𝑃−1 … 𝑤𝐻𝑃−𝑁𝐶−1

] [

𝑣(𝑘)

𝑣(𝑘 + 1)⋮

𝑣(𝑘 + 𝑁𝐶 − 1)

].

(4.32)

In compact form, (4.31) and (4.32) can be written as the following relations:

�� = ��𝑜 + 𝐺∆𝑅𝑜, (4.33)

��0 = 𝐶𝐴𝑥0 +𝑊𝑣. (4.34)

Being the prediction error e determined using the following equation,

𝑒 = 𝑦 − 𝑟𝑑 , (4.35)

where rd is the set-point. Substituting (4.33) in (4.35), and the result in (4.30), the objective

function can be presented in the form,

𝐽(∆𝑅𝑜) = (𝑌�� + 𝐺∆𝑅𝑜 − 𝑅𝑑)𝑇𝑄(��𝑜 + 𝐺∆𝑅𝑜 − 𝑅𝑑) + ∆𝑅𝑜

𝑇𝑅∆𝑅𝑜. (4.36)

The solution minimising J to give the optimal suggested control increment 𝑅𝑜∗, in the absence of

constrains, is given by 𝜕𝐽

𝜕Δ𝑅𝑜, resulting,

∆𝑅𝑜∗ = (𝐺𝑇𝑄𝐺 + 𝑅)−1𝐺𝑇𝑄(𝑅𝑑 − 𝑌��). (4.37)

To simulate the system it was considered, that the house dynamics is represented by (4.38) and

the PI controller by (4.39), respectively.

𝐾𝑃𝑙𝑎𝑛𝑡𝜏𝑃𝑙𝑎𝑛𝑡 𝑠 + 1

, (4.38)

𝐾𝑃𝐼 (1 +1

𝜏𝑃𝐼 𝑠). (4.39)

With 𝐾𝑃𝑙𝑎𝑛𝑡 and τ𝑃𝑙𝑎𝑛𝑡 are the house and 𝐾𝑃𝐼 and 𝜏𝑃𝐼the controller parameters. Applying the

above FT’s in Figure 4.1, and analysing in separated each one of the entries, with and without

perturbation, results the in next equations (4.40) and (4.41), respectivly.

𝐾𝑃𝑙𝑎𝑛𝑡𝜏𝑃𝐼 𝑠

𝜏𝑃𝐼 𝜏𝑃𝑙𝑎𝑛𝑡 𝑠2 + 𝜏𝑃𝐼 𝑠(1 + 𝐾𝑃𝑙𝑎𝑛𝑡𝐾𝑃𝐼) + 𝐾𝑃𝑙𝑎𝑛𝑡𝐾𝑃𝐼

, (4.40)


71

𝐾𝑃𝑙𝑎𝑛𝑡𝐾𝑃𝐼(1 + 𝜏𝑃𝐼 𝑠)

𝜏𝑃𝐼 𝜏𝑃𝑙𝑎𝑛𝑡 𝑠2 + 𝜏𝑃𝐼 𝑠(1 + 𝐾𝑃𝑙𝑎𝑛𝑡𝐾𝑃𝐼) + 𝐾𝑃𝑙𝑎𝑛𝑡𝐾𝑃𝐼

. (4.41)

Converting the system to discrete space–state model, the augmented space-state model is given

by Ai , Bi and Ci. resulting matrixes are presented in the following format.

[𝑥(𝑘 + 1)𝑢(𝑘)

] = [𝐴 𝐵0 𝐼

] [𝑥(𝑘)

𝑢(𝑘 − 1)] + [

𝐵𝐼] ∆𝑢(𝑘), (4.42)

𝑦(𝑘) = [𝐶 0] [𝑥(𝑘)

𝑢(𝑘 − 1)], (4.43)

where A, B and C results from continuous to discrete space-state transformation using Zero

Order Hold (ZOH) (Rugh, 1996).

According to the above showed, the equations (4.33) and (4.34) parameters can assume now the

final form and can be written as follow.

𝐶𝐴 =

[ 𝐶𝑖𝐴𝑖 𝐶𝑖𝐴𝑖 … 𝐶𝑖𝐴𝑖𝐶𝑖𝐴𝑖

2 𝐶𝑖2𝐴𝑖2 ⋱ 𝐶𝑖𝐴𝑖

2

⋮ ⋮ ⋱ ⋮𝐶𝑖𝐴𝑖

𝐻𝑃 𝐶𝑖𝐴𝑖𝐻𝑃 … 𝐶𝑖𝐴𝑖

𝐻𝑃] , (4.44)

𝐺 =

[

𝐶𝑖1𝐵1𝑖 0 0 … … 0𝐶𝑖𝐴𝑖𝐵1𝑖 𝐶𝑖1𝐵1𝑖 0 … … 0

𝐶𝑖𝐴𝑖2𝐵1𝑖 𝐶𝑖𝐴𝑖𝐵1𝑖 𝐶𝑖1𝐵1𝑖 0 … ⋮⋮ ⋮ ⋮ … … ⋮

𝐶𝑖𝐴𝑖𝐻𝑃−2𝐵1𝑖 𝐶𝑖𝐴𝑖

𝐻𝑃−3𝐵1𝑖 𝐶𝑖𝐴𝑖𝐻𝑃−4𝐵1𝑖 … 0 0


𝐻𝑃−2𝐵1𝑖 𝐶𝑖𝐴𝑖𝐻𝑃−3𝐵1𝑖 … 𝐶𝑖𝐴𝑖𝐵1𝑖 𝐶𝑖1𝐵1𝑖]

, (4.45)

𝑊 =

[

𝐶𝑖1𝐵2𝑖 0 0 … … 0𝐶𝑖𝐴𝑖𝐵2𝑖 𝐶𝑖1𝐵2𝑖 0 … … 0

𝐶𝑖𝐴𝑖2𝐵2𝑖 𝐶𝑖𝐴𝑖𝐵2𝑖 𝐶𝑖1𝐵2𝑖 0 … ⋮⋮ ⋮ ⋮ … … ⋮


𝐻𝑃−3𝐵2𝑖 𝐶𝑖𝐴𝑖𝐻𝑃−4𝐵2𝑖 … 0 0


𝐻𝑃−2𝐵2𝑖 𝐶𝑖𝐴𝑖𝐻𝑃−3𝐵2𝑖 … 𝐶𝑖𝐴𝑖𝐵2𝑖 𝐶𝑖1𝐵2𝑖]

, (4.46)

where B1i and B2i emerge from matrix Bi corresponding each one to one of the system inputs.

Rewriting (4.33) and (4.34) results in,

�� = 𝑌�� + 𝐺∆𝑅0 , (4.47)

𝑌�� = 𝛤𝑦𝜁(𝑘) +𝑊𝑦𝑣. (4.48)

From matrices T(C, ��) and L(C, ��, ��) below,


72

𝑻(��, ��) = [

��2

⋮��𝐻𝑃

], (4.49)

ℒ(��, ��, ��)=

[

�� 0 … 0�� … 0��2�� 0 ⋮⋮ ⋮ … ⋮

��𝐻𝑃−2�� 𝐻𝑃−3�� … 0��𝐻𝑃−1�� 𝐻𝑃−2�� … ��]

. (4.50)

The matrices G, Wy and Γy can be obtained and formalized as:

𝛤𝑦 = T(𝐶𝑦, 𝐴1), 𝛤𝑢 = T(𝐶𝑢 , 𝐴1), (4.51)

𝑊𝑦 = ℒ(𝐶𝑦 , 𝐴1, 𝐵2) and 𝑊𝑢 = ℒ(𝐶𝑢, 𝐴1, 𝐵2), (4.52)

𝐺 = ℒ(𝐶𝑦 , 𝐴1, 𝐵1), 𝐺𝑢 = ℒ(𝐶𝑢 , 𝐴1, 𝐵1). (4.53)

As mentioned above, the control is now made with constrains to find the r0(k) that minimize

the cost function presented in (4.54). Assuming that the available energy is conditioned, the

control method intent to restrict the value of the heating/cooling user power demanding, u. The

designed, Figure 4.2 system also includes constrains in upper and lower value of r0 and r0.

1B(q-1)1+ + y(k)

v(k)

A(q-1)AC(q-1)

B2C(q-1)

B1C(q-1)RG

r(k) r0(k)

+

-

u(k)

+

HomeHome

Controller

Governor 1

Figure 4.2. MPC with constraints, system block diagram.

The predictive controller can be posed as a quadratic programming problem, where,

𝑚𝑖𝑛∆𝑅0

𝐽(𝑘) = (𝑌�� + 𝐺∆𝑅0 − 𝑅𝑑)𝑇𝑄𝑒(𝑌�� + 𝐺∆𝑅0 − 𝑅𝑑) + ∆𝑅0

𝑇𝑅𝑒∆𝑅0, (4.54)


73

is to be optimized, subject to the constraints (4.55)-(4.59):

𝑦(𝑘) = 𝐴(𝑞−1)𝑦(𝑘 − 1) + 𝐵(𝑞−1)𝑢(𝑘 − 1) + 𝐶(𝑞−1)𝑣(𝑘 − 1), (4.55)

𝑢(𝑘) = 𝐴𝑐(𝑞−1)𝑢(𝑘 − 1) + 𝐵1𝑐(𝑞

−1)𝑟0(𝑘) − 𝐵2𝑐(𝑞−1)𝑦(𝑘), (4.56)

𝑟𝑜(𝑘) ≤ 𝑟𝑜(𝑘) ≤ 𝑟𝑜(𝑘), (4.57)

∆𝑟𝑜(𝑘) ≤ ∆𝑟𝑜(𝑘) ≤ ∆𝑟𝑜(𝑘), (4.58)

𝑢(𝑘) ≤ 𝑢(𝑘) ≤ 𝑢(𝑘). (4.59)

Developing (4.54), the new cost function can be written as (Igreja and Cruces, 2002)


𝐽 = (1

2∆𝑅0

𝑇𝑄𝑢∆𝑅0) + 𝐶𝑢𝑇∆𝑅0, (4.60)

with

𝑄𝑢 = 2(𝐺𝑇𝑄𝑒𝐺 + 𝑅𝑒), (4.61)

And

𝐶𝑢𝑇 = −2(𝑅𝑑 − 𝑌��)

𝑇𝑄𝑒 . 𝐺. (4.62)

The constrains can be expressed in terms of control movements resulting,

𝑅0 ≤ 𝑇𝑙∆𝑅0 + [𝐼𝑚 … 𝐼𝑚]𝑟𝑜(𝑡 − 1) ≤ 𝑅0 , (4.63)

∆𝑅0 ≤ ∆𝑅 ≤ ∆𝑅0, (4.64)

𝑈 ≤ 𝐺∆𝑅0 + 𝑈�� ≤ 𝑈, (4.65)

where Tl is a lower triangular matrix whose non null submatrices are Im the identity matrix.

Introducing the new variable,

𝑋 = 𝑇𝑙∆𝑅𝑜 + 𝛱 . (4.66)

𝛱 = [𝐼𝑚 …𝐼𝑚]𝑟𝑜(𝑘 − 1) − 𝑅0. (4.67)

∆Ro becomes,

∆𝑅𝑜 = 𝑉(𝑋 − 𝛱), (4.68)


74

𝑉 = 𝑇𝑙−1. (4.69)

And consequently (4.60) becomes,


𝐽 = (1

2𝑋𝑇𝑄𝑋𝑋) + 𝐶𝑋

𝑇𝑋, (4.70)

𝑄𝑥 = 𝑉𝑇𝑄𝑢𝑉 = 2𝑉

𝑇(𝐺𝑇𝑄𝑒𝐺 + 𝑅𝑒)𝑉, (4.71)

and

𝐶𝑥𝑇 = 𝐶𝑢

𝑇 − 𝛱𝑇𝑉𝑇𝑄𝑢𝑉 = −2𝛱𝑇𝑉𝑇(𝐺𝑇𝑄𝑒𝐺 + 𝑅𝑒)𝑉. (4.72)

Finally, the constrains can be expressed as,

[ 𝐼−𝑉𝑉

−𝐺𝑢𝑉𝐺𝑢𝑉 ]

𝑋 ≤

[ 𝑅0 − 𝑅0

−∆𝑅0 − 𝑉𝛱

∆𝑅0 + 𝑉𝛱

−𝑈 − 𝐺𝑢𝑉𝛱 + ��𝑂

𝑈 + 𝐺𝑢𝑉𝛱 − ��𝑂 ]

. (4.73)

The QP solution can be obtained using a modified Lemke’s method (Camacho, 1993; Igreja and

Cruces, 2002).

Remark: the predicted needed power is given by (4.74).

��𝑂 = 𝛤𝑢𝜁(𝑘) +𝑊𝑢𝑣, (4.74)

where, the only active state in 𝛤𝑢 is the one that corresponds to u in ζ(𝑘). Matrices Wu and Γu

are showed in annex. With this formalization, constrains can be directly applied taking into

account the limited power variation along time.

4.3 Results

As mentioned, it was created a temperature “comfort zone”. This approach allows to weight

only the temperatures outside the gap, instead of traditional system were all deviations are

weight, and consequently, more resources are needed. Also, in order to reduce the energy needs,

it was defined that u(k)=0 inside the temperature bound. It is considered a comfort zone if the

indoor reference is eT relatively to the reference temperature. Two situations are here presented

and the obtained results can be seen in Chapter 4.3.2. In the first situation is considered that

outside the comfort zone, the system calculates u(k) and the cost function J, and, inside the

comfort zone both u and J are null. The second situation it is distinguished from the first one


75

because it considers that inside the comfort zone, the cost function J can always assume the

optimal value.

The generalised cost function can be written as (4.75).

𝐽(𝑘) =∑‖𝑒(𝑘 + 𝑙)‖𝑄𝑒2 +

𝐻𝑃

𝑙=1

∑‖𝛥𝑟0(𝑘 + 𝑙 − 1)‖𝑅𝑒2

𝑁𝐶

𝑙=1

], (4.75)

where Qe ≥0 and Re >0 are weight matrices and depend from eT., HP, NC are predictive

horizon and control horizon, respectively, with HP ≥ M and, Δr0(k) is the input increment

vector.

As mentioned, Qe and Re depend on eT value.

𝑄𝑒 {0 ‖𝑒‖ ≤ 𝑒𝑇𝑄 ‖𝑒‖ > 𝑒𝑇

(4.76)

𝑅𝑒 {0 ‖𝑒‖ ≤ 𝑒𝑇𝑅 ‖𝑒‖ > 𝑒𝑇

. (4.77)

In the simulated system it is considered that the house is exposed to an additional perturbation,

solar incidence, which elevates the outside temperature in more 7 ºC between 15 and 19 hours,

Figure 4.3.

Figure 4.3. Outdoor temperature.

The simulation period is 48 hours and the several approaches are compared. The results are

showed in the next subsections and the used parameters are in the table below.

5 10 15 20 25 30 35 40 4510

15

20

25

30

35

Time (h)

Tem

pera

ture

(ºC

)

Outdoor Temp.


76

Table 4.1.Simulation parameters for PIvsMPC

Parameter Value Units

HP 24 -

NC 48 -

∆t 0.5 h

KPlant 1 -

Plant 130 -

R 0.1 -

Q 1 -

PI gain (KPI) 200 -

PI time const (PI) 130 s

eT 0.5 ºC

4.3.1 PI versus MPC.

The results and performance with PI controller and with MPC+PI are here analysed, compared

and showed in Figure 4.4 to Figure 4.6.

Figure 4.4. Indoor temperature.

5 10 15 20 25 30 35 40 4518

18.5

19

19.5

20

20.5

21

21.5

22

Time (h)

Tem

pera

ture

(ºC

)

Temp. Ref.

Indoor Temp (PI)

Indoor Temp (MPC+PI)

Generated Ref (MPC+PI).


77

Figure 4.5. Power and energy consumption.

Figure 4.6. Temperature error with and without (MPC).

As can been seen in Figure 4.5 the total energy consumption is very similar, but, the MPC

provides the anticipative effect, Figure 4.4, that maintains the indoor temperature always in line

with the reference minimizing the error, Figure 4.6, comparatively with the PI solution.

4.3.2 MPC with “comfort zone”

As mentioned, here are present the obtained results of two distinguish situations. The “Case 1”

considered that outside the comfort zone u and the cost function are calculated and inside

comfort zone both u and J are null.

The second approach, “Case 2”, is similar to the first but the cost function J is always

calculated.

5 10 15 20 25 30 35 40 45-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

Time (h)

Contr

ol In

put

(kW

) | E

nerg

y (

kW

h/1

0)

Control Input U (PI)

Control Input U (MPC+PI)

Energy(PI)

Energy (MPC+PI)

5 10 15 20 25 30 35 40 450

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Time (h)

e2 (

ºC)

e2 (with MPC)

e2 (without MPC)


78

The next table summarize the actions that distinguish both approaches.

Table 4.2. Simplified algorithm for MPC with “comfort zone”.

Case 1 Case 2

if ‖𝑒‖ > 𝑒𝑇(0.5º𝐶) then compute u and J

else

u=0 and J=0

end if

if ‖𝑒‖ > 𝑒𝑇(0.5º𝐶) then compute u and J

else

u=0

compute J

end if

Figure 4.7 and Figure 4.9 show the results

Figure 4.7. Case 1 - Indoor temperature with “comfort zone”.

Figure 4.8. Case 2 - Indoor temperature with “comfort zone”.

5 10 15 20 25 30 35 40 4518

19

20

21

22

23

24

25

26

27

28

Time (h)

Te

mp

era

ture

(ºC

)

Temp. Ref.

Indoor Temp (Case 1)

Generated Ref (Case 1)

5 10 15 20 25 30 35 40 4518

19

20

21

22

23

24

25

26

27

28

Time (h)

Te

mp

era

ture

(ºC

)

Temp. Ref.

Indoor Temp (Case 2)

Generated Ref (Case 2)


79

Figure 4.7 shows that the generated reference “Case 1” is constant (no optimal increment is

calculated) when the difference between temperatures is within the range, and, due this fact, the

MPC anticipative effect is lost.

Figure 4.9. Power and energy consumption with “comfort zone”.

On the other hand in Figure 4.7 the anticipative effect is maintain in “Case 2”, and

consequently, Figure 4.9 reveals better results with less power “peaks” and also with less energy

expended comparatively with “Case 1”.

4.3.3 MPC with “comfort zone” and constrained available power

The results presented in this item consider that the available power is limited and variable.

Figure 4.10. Indoor temperature evolution with limited power.

5 10 15 20 25 30 35 40 45-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time (h)

Co

ntr

ol In

put

(kW

) | E

nerg

y (

kW

h)

Control Input U (Case 1)

Control Input U (Case 2)

Energy (Case 1)

Energy (Case 2)

5 10 15 20 25 30 35 40 4518

19

20

21

22

23

24

25

26

Time (h)

Tem

pera

ture

(ºC

)

Temp. Ref.

Generated Ref.

Indoor Temp.


80

Figure 4.11. Power and energy consumption with limited power.

In Figure 4.10 can be seen that due the constrained power, Figure 4.11, the indoor temperature

cannot always follow the reference. The amount of energy expended grows a bit comparatively

with Figure 4.9.

4.3.4 Conclusions

In this chapter, in order to provide thermal house comfort, a MPC control technique associated

with a inner loop PI was presented.

It could be observed through the simulations and analysis results that good performances were

obtain by both approaches (with and without MPC). In general the error and the energy

consumption were considerably reduced with the MPC implementation.

In particular, results show that in the “comfort zone” MPC controller reduces considerably the

energy consumption with less power “peaks”.

The MPC power constrained shows that the approach can find a fair trade-off due to the

combination of the anticipative effect with available power, in order to maintain the temperature

near to the comfort zone, even when indoor temperature cannot follow the desire reference.

5 10 15 20 25 30 35 40 45-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Time (h)

Contr

ol In

put

(kW

) | E

nerg

y (

kW

h)

Control Input U

Umax

Umin

Energy

81

Chapter 5

5 Thermal Comfort with Demand Side

Management Using Distributed MPC

5.1 Introduction

Emerging new technologies like distributed generation, distributed storage, and demand-side

load management will change the way we consume and produce energy. These techniques

enable the possibility to reduce the greenhouse effects and improve grid stability, balancing the

demand and supply. Also, the reduction in CO2 emissions and the introduction of renewable

sources based generation have become important topics today. However, these renewable

resources are mainly given by very fluctuating and uncontrollable sun, water, and wind power.

The work here presented intends to support the expected introduction of a large penetration

level of renewable sources, in particularly providing a solution for implementation in an

environment where buildings are mainly supplied by this type of resource. Especially because,

reducing energy consumption in buildings is a trend in the world today due to economic aspects

or environmental reasons. This chapter presents a DMPC for indoor thermal comfort which

simultaneously optimizes the consumption of a limited shared energy resource. The control

objective of each subsystem is to minimize the heating/cooling energy cost while maintaining

the indoor temperature and consumed power inside bounds. In a distributed coordinated

environment, the control uses multiple dynamically coupled agents (one for each

subsystem/house) aiming to achieve satisfaction of coupling constraints. In accordance with the

hourly power demand profile, each house assigns a priority level indicating how much is willing

to bid in auction for consumption of limited clean resource. This procedure allows the hourly

variation of bidding values and, consequently, agent’s orders for accessing clean energy also

THERMAL COMFORT WITH DEMAND SIDE MANAGEMENT USING DISTRIBUTED MPC

82

varies. Despite of power constraints, all houses also have thermal comfort constraints that must

be fulfilled. The system is simulated with several houses in a distributed environment.

5.2 Implemented global scenario

The scenario considers two types of available energy resources, the green and the red. The

green or clean resource must always be consumed (it is not disposable), it is limited to a

maximum available value and it is considered a time variable resource. In opposition, the red is

always available and it is considered a dirty resource, more expensive than the green. Therefore,

if the green resource is insufficient to satisfy the house’s required demand, the red must be

consumed with an increase in the total energy cost. To encourage clean resource consumption, it

is considered that green energy price per kWh has a maximum auction value and it is always

cheaper than the red energy price. The agents (one by each house) must bid in an auction

(provided by the MO), the price that they are willing to pay to consume the green resource. The

agents make their bid in the auction with one day ahead to show how much is intended to pay

per kWh to consume green resource in each one of the next 24 hours. The next dots summarize

all assumptions made:

Divisions must share a limited predictable renewable green resource;

The green or clean resource must always be consumed or stored and it is limited to

a maximum available that varies in time.

Agents make their bid in the auction with one day ahead to show how much is

intended to pay per kWh for consumption of green resource, in each one of the

next 24 hours;

Access to green resource is done hourly in accordance to the made bid value. The

one that is able to pay more uses the needed stock first, and the second can use only

the remaining energy, and so on;

Outside temperatures, disturbances and daily comfort temperature bounds are

known by each system inside the predictive horizon (HP);

If the green resource is insufficient to satisfy the demand required by the

houses/divisions, the red resource (from grid) must be consumed;

The red resource has a fixed kW price that is always higher than the green to

promote the renewable energy consumption;

DMPC FOR THERMAL HOUSE COMFORT WITH SEQUENTIAL ACCESS AUCTION

83

The consumed red resource for comfort purposes implies a penalty in the final cost

function (5.1) due to the soft constraint violation, which is imposed by the

maximum available green resource if exceeded.

The MPC optimization is solved by each TCA at each time step according to the sequential

DMPC scheme depicted in Figure 5.1. The green available power forecast is received by the

agent who made the highest bid (first in the sequential access scheme) and this information is

used as power constraint value in (5.10). The agent optimization problem predicts the

consumption, subtracts it to the initially received available maximum and passes the information

to the next on the sequence list.

MPC 1

MPC 2

TCA 1

TCA 2

MPC NW -1 TCA NS -1

MPC NW TCA NS

uTgreen

*12 1TgreenU u u

*11 1

S

S S

NN NU U u

*iT

*iu

*23 3 1U U u

21u

11u

1

1SN

u

11v

21v

1

1SN

v

11T

21T

1

1SN

T

1SN

u

1SN

v

1SN

T

Figure 5.1. Implemented sequential architecture scheme.

In Figure 5.1, 𝑢𝑇𝑔𝑟𝑒𝑒𝑛 represents the green resource forecasts, 𝑈𝑖 the maximum available

expected green resource for TCA (i), 𝑇𝑖 and 𝑇𝑖∗ are the indoor temperature and indoor

temperature prediction, 𝑢𝑖 and 𝑢𝑖∗ are the optimal power generated by the MPC controller and

the predicted consumption and 𝑣𝑖 represents the disturbances.


84

5.3 MPC formalization

At each time step, each one of the agents must solve his MPC problem. The objectives are:

minimize the energy consumption to heating and cooling; minimize the peak power

consumption; maintain the zones within a desired temperature range and maintain the used

power within the green available bounds. Feedback stability is provided by choosing a

sufficiently long predictive horizon and proven by results presented in next shapters. Feasibility

is achieved by the use of soft constraints in the optimization problem formulation as explained

in the sequel.

The generic optimization problem to be solved by each agent at each instant, assumes the

following form:

𝑚𝑖𝑛𝑈,��,𝜀,��,𝛾

𝐽𝑖(𝑘) = ∑ [∑𝑢𝑙𝑖(𝑘 + 𝑗)𝑇𝜑𝑙

𝑖𝑢𝑙𝑖(𝑘 + 𝑗)⏟

𝐶𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛

𝑁𝑑𝑖

𝑙=1

]

𝐻𝑝−1

𝑗=0

+∑𝜙𝑖𝑚𝑎𝑥 {𝑢𝑙𝑖2(𝑘), . . . . , 𝑢𝑙

𝑖2(𝑘 + 𝐻𝑝 − 1)}⏟ 𝑃𝑜𝑤𝑒𝑟 𝑝𝑒𝑎𝑘𝑠

𝑁𝑑𝑖

𝑙=1

+∑[∑(𝜀𝑙𝑖(𝑘 + 𝑗)𝑇𝛯𝑙

𝑖𝜀𝑙𝑖(𝑘 + 𝑗⏟

𝐶𝑜𝑚𝑓𝑜𝑟𝑡 𝑣𝑖𝑜𝑙𝑎𝑡𝑖𝑜𝑛

) + 𝛾𝑙𝑖(𝑘 + 𝑗)𝑇𝛹𝑙

𝑖𝛾𝑙𝑖(𝑘 + 𝑗)⏟

𝑃𝑜𝑤𝑒𝑟 𝑣𝑖𝑜𝑙𝑎𝑡𝑖𝑜𝑛

)

𝑁𝑑𝑖

𝑙=1

]

𝐻𝑝

𝑗=1

,

(5.1)

𝑚𝑖𝑛𝑈𝑖,𝜀𝑖,𝛾𝑖

𝐽𝑖(𝑘) = 𝜀𝑖𝑇(𝑘)𝛯𝑖𝜀𝑖(𝑘) + 𝛾𝑖

𝑇(𝑘)𝛹𝑖𝛾𝑖(𝑘) + 𝑈𝑖𝑇(𝑘)𝑅𝑖𝑈𝑖(𝑘)

+∑𝜙𝑖𝑚𝑎𝑥 {𝑢𝑙𝑖2(𝑘), . . . . , 𝑢𝑙

𝑖2(𝑘 + 𝐻𝑝 − 1)}

𝑁𝑑𝑖

𝑙=1

, (5.2)

with,

𝑈𝑖(𝑘) =

[ 𝑈𝑖1(𝑘)

𝑈𝑖2(𝑘)⋮𝑈𝑖𝑁𝑑(𝑘)]

, (5.3)

𝜀𝑖(𝑘) =

[ 𝜀𝑖1(𝑘)

𝜀𝑖2(𝑘)

⋮

𝜀𝑖𝑁𝑑(𝑘)

𝜀𝑖1(𝑘)

𝜀𝑖2(𝑘)

⋮𝜀𝑖𝑁𝑑(𝑘)]

, 𝜀𝑖𝑙(𝑘) =

[ 𝜀𝑖𝑙(𝑘 + 1)

𝜀𝑖𝑙(𝑘 + 2)

⋮

𝜀𝑖𝑙(𝑘 + 𝐻𝑃)]

, 𝜀𝑖𝑙(𝑘) =

[ 𝜀𝑖𝑙(𝑘 + 1)

𝜀𝑖𝑙(𝑘 + 2)

⋮𝜀𝑖𝑙(𝑘 + 𝐻𝑃)]

, (5.4)

𝛾𝑖(𝑘) = [𝛾𝑖(𝑘)

𝛾𝑖(𝑘)], 𝛾

𝑖(𝑘) =

[ 𝛾𝑖(𝑘 + 1)

𝛾𝑖(𝑘 + 2)

⋮𝛾𝑖(𝑘 + 𝐻𝑃)]

, 𝛾𝑖(𝑘) =

[ 𝛾𝑖(𝑘 + 1)

𝛾𝑖(𝑘 + 2)

⋮𝛾𝑖(𝑘 + 𝐻𝑃)]

. (5.5)


85

Resulting in quadratic optimization problem in the compact form

𝑚𝑖𝑛 𝑍𝑖𝐽𝑖(𝑘) = 𝑍𝑖

𝑇𝛩𝑍𝑖 +∑𝜙𝑖𝑙𝑚𝑎𝑥 {𝑢𝑙𝑖2(𝑘), . . . . , 𝑢𝑙

𝑖2(𝑘 + 𝐻𝑝 − 1)}

𝑁𝑑𝑖

𝑙=1

. (5.6)

With

𝑍𝑖 = [𝑈𝑖𝜀𝑖𝛾𝑖

], 𝛩 = [

𝜑𝑖 0 00 𝛯𝑖 00 0 𝛹𝑖

], (5.7)

and subject to the following constraints,

𝑥𝑙𝑖(𝑘 + 𝑗 + 1) = 𝐴𝑙𝑙

𝑖𝑖𝑥𝑙𝑖(𝑘 + 𝑗) + 𝐵𝑙

𝑖𝑢𝑙𝑖(𝑘 + 𝑗) + ∑ (𝐴𝑙𝑔

𝑖𝑖 ��𝑙𝑖(𝑘 + 𝑗))

𝑁𝑑𝑖

𝑔=1(𝑔≠𝑙)⏟ 𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒𝑠 𝑓𝑟𝑜𝑚 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑎𝑟𝑒𝑎𝑠

𝑖𝑛𝑠𝑖𝑑𝑒 𝑡ℎ𝑒 𝑠𝑎𝑚𝑒 ℎ𝑜𝑢𝑠𝑒

+ ∑ ∑ (𝐴𝑙𝑚𝑖ℎ ��𝑚

ℎ (𝑘 + 𝑗))

𝑁𝑑ℎ

𝑚=1

𝑁𝑠

ℎ=1(ℎ≠𝑖)⏟ 𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒𝑠 𝑓𝑟𝑜𝑚 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑎𝑟𝑒𝑎𝑠

𝑓𝑟𝑜𝑚 𝑜𝑡ℎ𝑒𝑟 ℎ𝑜𝑢𝑠𝑒𝑠

+ 𝑣𝑙𝑖(𝑘 + 𝑗),

, 𝑗 = 1. . . 𝐻𝑃

(5.8)

𝑇𝑙𝑖(𝑘 + 𝑗) − 𝜀𝑙

𝑖(𝑘 + 𝑗) ≤ 𝑥𝑙𝑖(𝑘 + 𝑗) ≤ ��𝑙

𝑖(𝑘 + 𝑗) + 𝜀��𝑖(𝑘 + 𝑗), (5.9)

𝑈𝑖(𝑘 + 𝑗 − 1) − 𝛾𝑖(𝑘 + 𝑗 − 1) ≤∑𝑢𝑙𝑖(𝑘 + 𝑗 − 1)

𝑁𝑑𝑖

𝑙=1

≤ 𝑈𝑖(𝑘 + 𝑗 − 1) + ��𝑖(𝑘 + 𝑗 − 1), (5.10)

𝛾𝑖 , ��𝑖 , 𝜀𝑙𝑖, 𝜀��

𝑖 ≥ 0. (5.11)

In (5.1) 𝑁𝑑𝑖is the number of divisions of house (i), 𝑢𝑖𝑙 represents the power control inputs from

house (i) division (l), 𝜙𝑖is the penalty on peak power consumption, 𝛯𝑖 is the penalty on the

comfort constraint violation, Ψithe penalty on the power constraint violation and HP is the

length of the prediction horizon. In (5.9), 𝜀��𝑖 and 𝜀𝑙

𝑖 are the vectors of temperature violations that

are above and below the desired comfort zone defined by ��𝑙𝑖 and 𝑇𝑙

𝑖. In (5.10), the coupled

power constraint, 𝛾𝑖 and 𝛾𝑖are the power violations that are above or lower the maximum,𝑈𝑖,

and minimum, 𝑈𝑖, available green power for heating/cooling the house, with 𝑈𝑖 = −𝑈𝑖. Remark

that, in each TCA (i), the power sum in all divisions cannot exceed 𝑈𝑖 and that in (5.8) 𝑥𝑙𝑖∗and

𝑢𝑙𝑖∗represent the predicted temperature and power consumption within the prediction horizon.

With this approach each TCA can have different hourly penalties, allowing the consumer to

choose between more/less comfort and cost during the day as Figure 5.2 exemplify. This

procedure was implemented in Algorithm II.


86

Figure 5.2. Daily consumer profile.

An example of formulization is made for and distributed situation where two distinct TCA’s are

dynamically and constraints coupled.

1 2

1u

1y2u

2y

Figure 5.3. Thermally coupled TCA’s.

For TCA1 and TCA2 it can be written

{

𝐶1𝑒𝑞

1 ��11 = 𝑢1

1 +𝑇𝑜𝑎 − 𝑇1

1

𝑅1𝑒𝑞1 +

𝑇12 − 𝑇1

1

𝑅11𝑒𝑞12 + 𝑃1𝑃𝑑

1 ,

𝐶1𝑒𝑞2 ��1

2 = 𝑢12 +

𝑇𝑜𝑎 − 𝑇12

𝑅1𝑒𝑞2 +

𝑇11 − 𝑇1

2

𝑅11𝑒𝑞12 + 𝑃1𝑃𝑑

2

(5.12)

{

𝐶1𝑒𝑞

1 ��11 = 𝑢1

1 − (1

𝑅1𝑒𝑞1 +

1

𝑅11𝑒𝑞12 )𝑇1

1 +𝑇𝑜𝑎 − 𝑇1

1

𝑅1𝑒𝑞1 +

𝑇12

𝑅11𝑒𝑞12 +

𝑇𝑜𝑎

𝑅1𝑒𝑞1 +𝑃1𝑃𝑑

1

𝐶1𝑒𝑞2 ��1

2 = 𝑢12 − (

1

𝑅1𝑒𝑞2 +

1

𝑅11𝑒𝑞12 )𝑇1

2 +𝑇𝑜𝑎 − 𝑇1

2

𝑅1𝑒𝑞2 +

𝑇11

𝑅11𝑒𝑞12 +

𝑇𝑜𝑎

𝑅1𝑒𝑞2 +𝑃1𝑃𝑑

2

(5.13)

[��11

��12] =

[ −

𝑅1𝑒𝑞1 + 𝑅11𝑒𝑞

12

𝑅1𝑒𝑞1 𝐶1𝑒𝑞

1 𝑅11𝑒𝑞12

1

𝐶1𝑒𝑞1 𝑅11𝑒𝑞

12

1


12 −𝑅1𝑒𝑞2 + 𝑅11𝑒𝑞

12


2 𝑅11𝑒𝑞12

]

[𝑇11

𝑇12] +

[ 1

𝐶1𝑒𝑞1 0

01

𝐶1𝑒𝑞2]

[𝑢11

𝑢12] +

[ 𝑇𝑜𝑎


1 +𝑃1𝑃𝑑1

𝐶1𝑒𝑞1

𝑇𝑜𝑎


2 +𝑃1𝑃𝑑2

𝐶1𝑒𝑞2]

. (5.14)

For TCA 1 the plant model representation (5.14) can be rewritten and changed into a discrete

model using Euler discretization with a sampling time of Δt.

��11 =

𝑇(𝑘 + 1) − 𝑇(𝑘)

∆𝑡, (5.15)

00:00 23:0001:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00

ComfortConsumption Consumption Comfort Consumption Comfort

MAX - 23 ºC

MIN - 21 ºC

MAX - 22 ºC

MIN - 20 ºC

MAX - 21 ºC

MIN - 20 ºC


87

𝑇(𝑘 + 1) − 𝑇(𝑘)

∆𝑡= −


12


1 𝑅11𝑒𝑞12 ��1

1(𝑘) −1


12 𝑇12(𝑘) +

1

𝐶1𝑒𝑞1 𝑢1

1(𝑘) +1


1 𝑇𝑜𝑎(𝑘)

+1

𝐶1𝑒𝑞1 𝑃1𝑃𝑑

1 (𝑘), (5.16)

𝑇11(𝑘 + 1) = 𝐴11

11𝑇11(𝑘) + 𝐵1

1𝑢11(𝑘) + 𝐴11

12𝑇12(𝑘) + 𝑣1

1(𝑘), (5.17)

where

𝐴1 = 𝐴1111 = (1 −


12


1 𝑅11𝑒𝑞12 ∆𝑡), (5.18)

𝐷1 = 𝑣11 =

𝑃1𝑃𝑑1

𝐶1𝑒𝑞1 Δt +

Toa


1 Δt,

𝐵1 = 𝐵11 =

1

𝐶1𝑒𝑞1 𝛥𝑡,

𝐶1 = 𝐴1112 =

1


1 Δt.

For several instants, (5.17) can be written as follows,

𝑇11(1) = 𝐴1𝑇1

1(0) + 𝐵1𝑢11(0) + 𝐶1𝑇1

2(0) + 𝐷1(0), (5.19)

𝑇11(2) = (𝐴1)

2𝑇11(0) + 𝐴1𝐵1𝑢1

1(0) + 𝐴1𝐶1𝑇12(0) + 𝐴1𝐷1(0) + 𝐵1𝑢1

1(1) + 𝐶1𝑇12(1) + 𝐷1(1), (5.20)

𝑇11(3) = (𝐴1)

3𝑇11(0) + (𝐴1)

2𝐵1𝑢11(0) + (𝐴1)

2𝐶1𝑇12(0) + (𝐴1)

2𝐷1(0) + 𝐴1𝐵1𝑢11(1)

+ 𝐴1𝐶1𝑇12(1) + 𝐴1𝐷1(1) + 𝐵1𝑢1

1(2) + 𝐶1𝑇12(2) + 𝐷1(2), (5.21)

Therefore,

𝑀𝑎𝑡𝑈 =

[ 𝐵1 0 ⋯ ⋯ ⋯ 0𝐴1𝐵1 𝐵1 ⋱ ⋯ ⋯ ⋮

𝐴12𝐵1 𝐴1𝐵 𝐵1 ⋱ ⋯ ⋮

𝐴13𝐵1 𝐴1

2𝐵1 𝐴1𝐵1 𝐵1 ⋱ ⋮⋮ ⋮ ⋮ ⋮ 𝐵1 0

𝐴1𝐻𝑃𝐵1 𝐴1

𝐻𝑃−1𝐵1 ⋯ ⋯ 𝐴1𝐵1 𝐵1]

, (5.22)


88

𝑀𝑎𝑡𝑇𝑥 =

[ 𝐶1 0 ⋯ ⋯ ⋯ 0𝐴1𝐶1 𝐶1 ⋱ ⋯ ⋯ ⋮

𝐴12𝐶1 𝐴1𝐶1 𝐶1 ⋱ ⋯ ⋮

𝐴13𝐶1 𝐴1

2𝐶1 𝐴1𝐶1 𝐶1 ⋱ ⋮⋮ ⋮ ⋮ ⋮ 𝐶1 0

𝐴1𝐻𝑃𝐶1 𝐴1

𝐻𝑃−1𝐶1 ⋯ ⋯ 𝐴1𝐶1 𝐶1]

, (5.23)

𝑀𝑎𝑡𝐷 =

[ 1 0 ⋯ ⋯ ⋯ 0𝐴1 1 ⋱ ⋯ ⋯ ⋮

𝐴12 𝐴1 1 ⋱ ⋯ ⋮

𝐴13 𝐴1

2 𝐴1 1 ⋱ ⋮⋮ ⋮ ⋮ ⋮ 1 0𝐴1

𝐻𝑃 𝐴1𝐻𝑃−1 ⋯ ⋯ 𝐴1 1]

, (5.24)

𝑀𝑎𝑡𝑇 = [𝐴1 𝐴12 𝐴1

3 ⋯ 𝐴1𝐻𝑃].

(5.25)

It is considered that the constraints (5.9) and (5.10) must assume the form of Ax<B with,

𝑥 = [𝑢11; 𝜀1; 𝜀1; 𝛾1; ��1]

𝑇

,

(5.26)

where, ε1 and ε1 are the vectors of temperature violations that are above and below the desired

comfort zone defined by 𝑇11 and 𝑇1

1, and 𝛾1 and 𝛾1 are the power violations that are above or

lower the maximum.

Temperature constraints: 𝑇11(𝑘 + 1) = 𝐴1𝑇1

1(𝑘) + 𝐵1𝑢11(𝑘) + 𝐶1𝑇1

2(𝑘) + 𝐷1(𝑘),

𝑇11 − 𝜀1 ≤ 𝑇1

1 ≤ 𝑇11, +𝜀1,

(5.27)

𝑇11 −

[ 𝜀1(1)

𝜀1(2)

⋮⋮⋮𝜀1(𝐻𝑃)]

≤

[ 𝐴1𝐴1

2

𝐴13

⋮⋮𝐴1

𝐻𝑃]

𝑇11(0)

[ 𝐵1 0 ⋯ ⋯ ⋯ 0𝐴1𝐵1 𝐵1 ⋱ ⋯ ⋯ ⋮

𝐴12𝐵1 𝐴1𝐵 𝐵1 ⋱ ⋯ ⋮

𝐴13𝐵1 𝐴1

2𝐵1 𝐴1𝐵1 𝐵1 ⋱ ⋮⋮ ⋮ ⋮ ⋮ 𝐵1 0

𝐴1𝐻𝑃𝐵1 𝐴1

𝐻𝑃−1𝐵1 ⋯ ⋯ 𝐴1𝐵1 𝐵1]

[ 𝑢11(0)

𝑢11(1)⋮⋮⋮𝑢11(𝐻𝑃 − 1)]

+

[ 𝐶1 0 ⋯ ⋯ ⋯ 0𝐴1𝐶1 𝐶1 ⋱ ⋯ ⋯ ⋮

𝐴12𝐶1 𝐴1𝐶1 𝐶1 ⋱ ⋯ ⋮

𝐴13𝐶1 𝐴1

2𝐶1 𝐴1𝐶1 𝐶1 ⋱ ⋮⋮ ⋮ ⋮ ⋮ 𝐶1 0

𝐴1𝐻𝑃𝐶1 𝐴1

𝐻𝑃−1𝐶1 ⋯ ⋯ 𝐴1𝐶1 𝐶1]

[ 𝑇12(0)

𝑇12(1)⋮⋮⋮𝑇12(𝐻𝑃 − 1)]

+

(5.28)

[ 1 0 ⋯ ⋯ ⋯ 0𝐴1 1 ⋱ ⋯ ⋯ ⋮

𝐴12 𝐴1 1 ⋱ ⋯ ⋮

𝐴13 𝐴1

2 𝐴1 1 ⋱ ⋮⋮ ⋮ ⋮ ⋮ 1 0𝐴1

𝐻𝑃 𝐴1𝐻𝑃−1 ⋯ ⋯ 𝐴1 1]

[ 𝐷1(0)

𝐷1(1)⋮⋮⋮𝐷1(𝐻𝑃 − 1)]

≤ 𝑇11, +

[ 𝜀1(1)

𝜀1(2)⋮⋮⋮𝜀1(𝐻𝑃)]

.


89

Lower temperature constraint bound

𝑇11 − 𝜀1 ≤ 𝑇1

1, (5.29)

𝑇11 − 𝜀1 ≤ 𝑀𝑎𝑡𝑇 × 𝑇1

1 +𝑀𝑎𝑡𝑈 × 𝑢11 +𝑀𝑎𝑡𝑇𝑥 × 𝑇1

2 +𝑀𝑎𝑡𝐷 × 𝐷1, (5.30)

−(𝜀 +𝑀𝑎𝑡𝑈 × 𝑢11

⏟ 𝐴1

) ≤ −(𝑇11 −𝑀𝑎𝑡𝑇 × 𝑇1

1 +𝑀𝑎𝑡𝑇𝑥 × 𝑇12 +𝑀𝑎𝑡𝐷 × 𝐷1⏟

𝐵1

), (5.31)

𝐴1 = [𝑀𝑎𝑡𝑈𝐻𝑃×𝐻𝑃 𝐼𝐻𝑃×𝐻𝑃 0𝐻𝑃×𝐻𝑃 0𝐻𝑃×𝐻𝑃 0𝐻𝑃×𝐻𝑃]. (5.32)

Similarly, for the upper temperature bound can be written

𝑇11 ≤ 𝑇1

1+ 𝜀1, (5.33)

𝑀𝑎𝑡𝑇 × 𝑇11 +𝑀𝑎𝑡𝑈 × 𝑢1

1 +𝑀𝑎𝑡𝑇𝑥 × 𝑇12 +𝑀𝑎𝑡𝐷 × 𝐷1 ≤ 𝑇1

1+ 𝜀1, (5.34)

(𝜀1 +𝑀𝑎𝑡𝑈 × 𝑢11⏟

𝐴2

) ≤ −(𝑇11+𝑀𝑎𝑡𝑇 × 𝑇1

1 +𝑀𝑎𝑡𝑇𝑥 × 𝑇12 +𝑀𝑎𝑡𝐷 × 𝐷1⏟

𝐵2

), (5.35)

𝐴2 = [𝑀𝑎𝑡𝑈𝐻𝑃×𝐻𝑃 0𝐻𝑃×𝐻𝑃 − 𝐼𝐻𝑃×𝐻𝑃 0𝐻𝑃×𝐻𝑃 0𝐻𝑃×𝐻𝑃]. (5.36)

Power constraints also assume the form Ax<B, so to the lower bound,

𝑈1 − 𝛾1 ≤ 𝑈1, (5.37)

−𝛾1 − 𝑈1⏟ 𝐴3

≤ −𝑈1⏟𝐵3

, (5.38)

𝐴3 = [−𝐼𝐻𝑃×𝐻𝑃 0𝐻𝑃×𝐻𝑃 0𝐻𝑃×𝐻𝑃 − 𝐼𝐻𝑃×𝐻𝑃 0𝐻𝑃×𝐻𝑃]. (5.39)

Upper power constraint bound

𝑈1 ≤ ��1 + γ1, (5.40)

𝑈1 − γ1⏟ 𝐴4

≤ ��1⏟𝐵4

, (5.41)

A4 = [𝐼𝐻𝑃 ×𝐻𝑃 0𝐻𝑃×𝐻𝑃 0𝐻𝑃×𝐻𝑃 0𝐻𝑃×𝐻𝑃 − 𝐼𝐻𝑃×𝐻𝑃]. (5.42)

Finally for all soft constrains in the form of Ax<B results in,

[

−A1A2A3A4

] [𝑢11; ε1; ε1; γ1; γ1]

𝑇= [

−𝐵1𝑇

𝐵2𝑇

𝐵3𝑇

𝐵4𝑇

].

(5.43)


90

5.3.1 Algorithm I - Implemented sequential scheme

After the methodology description, the algorithm is described. As mentioned it is considered

that the sequence order was already stablished by a previous auction. The hourly access

sequence is storage in AO(NS×HP). Remark that, only the divisions that thermally interact pass to

each other the information about future indoor temperatures prevision.

Algorithm I - DSM-DMPC Implemented sequential scheme

Required for all TCA’s: Thermal disturbances, comfort temperature gap, hourly constraints

parameters and auction bid.

For all TCA’s Wi initialize:

BV bid value inside the HP PH1

for k=1 to NC

for i=1 to NS(the number of TCA’s)

Apply to all TCA 𝑢𝑙𝑖 (𝑘 − 1: 𝑘 − 1 + 𝐻𝑃) from k-1 instant to obtain 𝑇𝑙

𝑖(𝑘: 𝑘 +𝐻𝑃)

Communicate temperature predictions to adjacent TCA’s

Update available green resource

Calculate the optimal control sequence 𝑢𝑙𝑖(1:HP) solving OPi (5.1)-(5.11) with power constraints

(5.10) given by 𝑈𝑖 and ��𝑖

Update available green resource values for next TCA

��𝑖+1(𝑘: 𝑘 + 𝐻𝑃) = ��𝑖(𝑘: 𝑘 + 𝐻𝑃) −∑𝑢𝑙𝑖(𝑘: 𝑘 + 𝐻𝑃)

𝑁𝑑𝑖

𝑙=1

end for

end for

Remark: generically, 𝑋(𝑘: 𝑘 + 𝐻𝑃) represents a line vector (1 × 𝐻𝑃) containing values from

𝑥(𝑘) to 𝑥(𝑘 + 𝐻𝑃), and 𝑌(𝑝, 𝑘: 𝑘 + 𝐻𝑃), represents the line p of a matrix (𝑃 × 𝐻𝑃) containing

values from y(𝑝, 𝑘) to y(𝑝, 𝑘 + 𝐻𝑃).

91

Chapter 6

6 DMPC for Thermal House Comfort

with Sequential Access Auction

6.1 Introduction

This chapter presents, in a model predictive control multi-agent systems context, an integrative

methodology to manage energy networks from the demand side with strong presence of

intermittent energy sources and with energy storage in house-hold or car batteries. In particular

is presented a distributed model predictive control solution for indoor comfort that

simultaneously optimizes the usage of a limited shared energy resource via a demand side

management perspective (Barata et al., 2012b). The control is applied individually to a set of

Thermal Control Areas, demand units, where the objective is to minimize the energy cost while

maintaining the indoor temperature inside a comfort zone, without exceeding the limited and

shared energy resource. The Thermal Control Areas are generally thermodynamically connected

in the distributed environment and also are coupled by energy related constraints. The overall

system predicts indoor environmental conditions in buildings with different plans which are

modelled using an electro-thermal modular scheme (Chapter 3.4). For control purposes, this

modular scheme allows an easy modelling of buildings with different plans where adjacent

areas can thermally interact.

The results are presented with two different approaches. In Chapter 6.2, the energy split

performance is based on a fixed sequential order, established from a previously done auction

wherein the bids are made by each Thermal Control Area, acting as demand side management

agents and based on the energy daily price. In Chapter 6.3, bids can be made in accordance to


92

the consumption needs. Each TCA has an hourly known consumption profile and the bid value

is directly related to that consumption behaviour. Thus, to the assumptions made in Chaper 5.2

the next dots are added, stipulating the incremented specificities made in this chapter:

Green resource which is not consumed at the final of a certain instant is stored in

batteries up to capacity value (BcV). When BcV is reached it is considered that the

remaining green resource is delivered to the grid;

The access order to green resource varies hourly;

Each TCA has a known fixed 24 hours consumption profile, 𝐶𝑤𝑙𝑖(𝑘: 𝑘 + 𝐻𝑃) and it

is established a priority level from 1 (low) to 3 (high) for each hour indicating how

important it is to have available resource to supply the load;

The bid value of each house is made in accordance with the chosen priority level,

the hours with higher priority levels indicate high consumption and consequently a

higher bid value;

The access to green resource is done hourly in accordance with the made bid value.

The one that is able to pay more uses the needed stock first and the second can use

only the remaining energy, and so on.

The cost function penalty values may hourly vary;

The developed solutions are explained by Algorithm II and are applied to different scenarios

wherein the results illustrate the benefits of the proposed approach.

6.2 Access order with fixed stablished sequence

To explain and prove the concept, simulation results were made in accordance with the scheme

presented in Figure 6.2.

Figure 6.1: Heat transfer between divisions example.


93

Figure 6.2: System implementation scheme block diagram.

Three houses are considered, two of them thermally interacting (with a thermal resistance

between them of R12=30ºC/kW as shown in Figure 6.1 and the third is isolated.

6.2.1 Results

It is considered that all TCA´s have the same outdoor temperature presented in Figure 6.3.

Figure 6.3. Outdoor temperature forecasting.

The thermal characteristics and prices for all agents and scenarios are presented in Table 6.1.

House 3

House 1

SYSTEM DYNAMICALLY COUPLED

AND COUPLED BY CONSTRAINTS SYSTEM ONLY COUPLED BY CONSTRAINTS

House 2

0 5 10 15 2015

20

25

30

35

40

Time (h)

Te

mp

era

ture

(ºC

)

Temp. Outside


94

Table 6.1. Distributed parameters

Parameter A1 A2 A3 Units

Req 50 50 75 ºC/kW

Ceq 9.2103 9.2103 9.2103 kJ/ºC

Green Price (per kWh) 0.09 0.08 0.07 €

Red Price(per kWh) 0.18 €

As mentioned, agents can also have distinct penalties on power and temperature constraints

violations, they can hourly privilege comfort or cost according to consumer choice. Therefore,

to explore the concept several scenarios are here presented.

6.2.1.1 Scenario I - Balanced parameterization

The first, it is considered a balanced scenario, with no energy storage and no explicit preference

between comfort or consumption. Table 6.2 shows the penalty values that are used in the first

scenario.

Table 6.2. Scenario I - Penalty values

Parameter A1 A2 A3

𝛯 50 50 50

100 100 30

ϕ 2 2 2

1 1 1

The thermal disturbances forecasts and the indoor temperature with its constraints for the TCA,

A1, A2 and A3 have the profile presented in Figure 6.4, Figure 6.5 and Figure 6.6 respectively.

Figure 6.4. Scenario I - Disturbance forecasting and indoor temperature A1.

0 5 10 15 200

0.5

1

1.5

2

Pow

er

(kW

)

0 5 10 15 2018

19

20

21

22

23

Time (h)

Tem

pera

ture

(ºC

)

Indoor Temp. (ºC) Temp. Max (ºC) Temp. Min (ºC)

Disturbance Load A1 (kW)


95



Figure 6.7. Scenario I - A1 power profile.

0 5 10 15 2021

21.5

22

22.5

23

23.5

24

Time (h)

Tem

pera

ture

(ºC

)

0 5 10 15 200

0.5

1

1.5

2

Pow

er

(kW

)



0 5 10 15 200

0.5

1

1.5

2

2.5

3

Pow

er

(kW

)

0 5 10 15 2020

21

22

23

24

25

Time (h)

Tem

pera

ture

(ºC

)



0 5 10 15 20-2

-1

0

1

2

3

Pow

er

(kW

)

0 5 10 15 200

0.5

1

1.5

2

2.5

Time (h)

Pow

er

(kW

)

Power Max (kW) Power Min (kW) Consumption (kW)

Total Available (kW) Red Resource (kW) Green Resource (kW)


96

Despite the thermal disturbances, it can be seen in that the indoor temperatures are

predominantly inside their narrow bounds. The Figure 6.7, Figure 6.8 and Figure 6.9 show, for

TCA, A1, A2 and A3 respectively, the used power to acclimatize the spaces and the available

green resource to do it. The figures also show the amount and the type of the consumed power.



The power consumption behaviour shows that the controllers try to consume only when the

green resource is available. The compromise between comfort and consumption is notorious,

the controllers are always attempting to accomplish both constraints, but when is not possible it

compensates with one inside range and the other outside.

0 5 10 15 20-2

-1

0

1

2

Pow

er

(kW

)

0 5 10 15 200

0.5

1

1.5

2

Time (h)

Pow

er

(kW

)

Red Resource (kW) Green Resource (kW) Total Available (kW)

Power Max (kW) Consumption (kW) Power Min (kW)

0 5 10 15 20-2

-1

0

1

2

Pow

er

(kW

)

0 5 10 15 200

0.5

1

1.5

2

Time (h)

Pow

er

(kW

)

Consumption (kW) Power Max (kW) Power Min (kW)



97

Figure 6.10. Scenario I - Global consumption characterization.

Figure 6.11. Scenario I - Power profile.

Figure 6.12. Scenario I - Heating/cooling total cost.

0 5 10 15 200

0.5

1

1.5

2

2.5

Time (h)

Po

we

r (k

W)

Total Available (kW)

Total Red (kW)

Total Green (kW)

0 5 10 15 200

5

10

15

Time (h)

Pow

er

(kW

)

House 1 (kW)

House 2 (kW)

House 3 (kW)

0 5 10 15 200

0.2

0.4

0.6

0.8

1

1.2

Time (h)

Cost

(€)

House 3

House 1

House 2


98

Being the last in the sequence, A3 receives merely the remainder resource, which in several

periods is null obliging to a major consumption of red resource. Due this situation, despite A3

having the lowest consumption, Figure 6.11, is the one that have the highest cost Figure 6.12.

6.2.1.2 Scenario II - Balanced parameterization with storage

The second scenario intends to show the benefit of having energy storage, been the only

difference with Scenario I the increment of a set of batteries with 1.5 kWh of capacity, Figure

6.22. The thermal disturbances forecasts and the indoor temperature with its constraints for the

TCA, A1, A2 and A3 in this Scenario II, have the profile presented in Figure 6.13, Figure 6.14

and Figure 6.15 respectively.

Figure 6.13. Scenario II - Disturbance forecasting and indoor temperature A1.


0 5 10 15 200

0.5

1

1.5

2

Pow

er

(kW

)

0 5 10 15 2018

19

20

21

22

23

24

Time (h)

Tem

pera

ture

(ºC

)

Disturbance Load A1(kW)


0 5 10 15 200

0.5

1

1.5

2

Pow

er

(kW

)

0 5 10 15 2021

21.5

22

22.5

23

23.5

24

Time (h)

Tem

pera

ture

(ºC

)




99


Figure 6.16. Scenario II – A1 power profile.


0 5 10 15 200

1

2

3

Pow

er

(kW

)

0 5 10 15 2020

21

22

23

24

25

Time (h)

Tem

pera

ture

(ºC

)



0 5 10 15 20

-4

-2

0

2

4

6

Pow

er

(kW

)

0 5 10 15 200

1

2

3

4

5

Time (h)

Pow

er

(kW

)



0 5 10 15 20

-4

-2

0

2

4

6

Pow

er

(kW

)

0 5 10 15 200

0.5

1

1.5

2

2.5

3

3.5

Time (h)

Pow

er

(kW

)




100


Despite the thermal disturbances, it can be seen in that the indoor temperatures are

predominantly inside their narrow bounds.

As expected, with this energy supplement the power constraint of all TCA’s was respected,

exceptionally in the interval between 12-15h in A3, where a small amount of red resource was

consumed.

Figure 6.19. Scenario II - Global consumption characterization.

Comparatively with Figure 6.10, Figure 6.19 shows that the red resource consumption was

significantly reduced. The agent that most benefit with this modification was A3, the energy

surplus allows it to consume almost exclusively green resource bought at lower bid price , and

thus, is the one that presents lesser costs, Figure 6.21.

0 5 10 15 20-4

-2

0

2

4

Pow

er

(kW

)

0 5 10 15 200

1

2

3

Time (h)

Pow

er

(kW

)



0 5 10 15 200

0.5

1

1.5

2

2.5

3

3.5

Time (h)

Po

we

r (k

W)


Total Red (kW)

Total Green (kW)


101

Figure 6.20. Scenario II - Power profile.

Figure 6.21. Scenario II - Heating/cooling total cost.

Figure 6.22. Scenario II - Batteries profile.

0 5 10 15 200

2

4

6

8

10

12

14

16

18

20

Time (h)

Pow

er

(kW

)

House 1 (kW)

House 2 (kW)

House 3 (kW)

0 5 10 15 200

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Time (h)

Cost

(€)

House 1

House 2

House 3

0 5 10 15 200

0.4

0.8

1.2

1.5

Time (h)

Po

we

r (k

Wh

)


102

6.2.1.3 Scenario III - Parameterization for cost benefits

In the third scenario the penalty values of the parameters related with consumption were

increased. The comfort issues are now less important, with the agents mainly concerned with

lower consumptions and in satisfy the power constraint. With this variation, the soft power

constraint was transformed in a hard constraint.

Table 6.3. Scenario III - Penalty values

Due the scarcity of green resource and the obligation to respect the power limits, A3 was the one

that presented lower consumptions, Figure 6.30, and consequently minor costs, but on the other

hand, the indoor temperature was the most penalized with the highest deviation from the chosen

comfort range. With this parameterization, the consumption profile always maintained inside

bounds, for all TCA’s, Figure 6.26, Figure 6.27 and Figure 6.28. Consequently, in Figure 6.29

can be seen that any or negligible red resource was consumed.

Figure 6.23. Scenario III - Disturbance forecasting and indoor temperature A1.

0 5 10 15 200

0.5

1

1.5

2

Pow

er

(kW

)

0 5 10 15 2018

19

20

21

22

23

Time (h)

Tem

pera

ture

(ºC

)



Parameter A1 A2 A3

𝛯 50 50 50

100000 100000 30000

ϕ 20 20 20

10 10 10


103



Figure 6.26. Scenario III – A1 power profile.

0 5 10 15 200

0.5

1

1.5

2

Pow

er

(kW

)

0 5 10 15 2021

21.5

22

22.5

23

23.5

24

Time (h)

Tem

pera

ture

(ºC

)



0 5 10 15 200

0.5

1

1.5

2

2.5

3

Pow

er

(kW

)

0 5 10 15 2020

21

22

23

24

25

Time (h)

Tem

pera

ture

(ºC

)



0 5 10 15 20-2

-1

0

1

2

3

Pow

er

(kW

)

0 5 10 15 200

0.5

1

1.5

2

2.5

Time (h)

Pow

er

(kW

)

Power Min (kW) Consumption (kW) Power Max (kW)



104



Figure 6.29. Scenario III - Global consumption characterization.

0 5 10 15 20-2

-1

0

1

2

Pow

er

(kW

)

0 5 10 15 200

0.5

1

1.5

2

Time (h)

Pow

er

(kW

)

Power Min (kW) Consumption (kW) Power Max (kW)


0 5 10 15 20-2

-1

0

1

2

Pow

er

(kW

)

0 5 10 15 200

0.5

1

1.5

2

Time (h)

Pow

er

(kW

)



0 5 10 15 200

0.5

1

1.5

2

2.5

Time (h)

Po

we

r (k

W)


Total Red (kW)

Total Green (kW)


105

Figure 6.30. Scenario III - Power profile.

Figure 6.31. Scenario III - Heating/cooling total cost.

Therefore the energy costs, Figure 6.31, decreased in all agents, namely 8%, 9% and 54%

comparatively with Scenario I, and 9%, 45% and 25% when compared with Scenario II, as

summarized in Table 6.4.

Table 6.4. Scenario III - Cost comparisons

Scenario A1 A2 A3

I 1,27 1,09 1,27

II 1,39 1,52 0,92

III 1,18 1,00 0,69

0 5 10 15 200

2

4

6

8

10

12

14

Time (h)

Po

we

r (k

W)

House 1 (kW)

House 2 (kW)

House 3 (kW)

0 5 10 15 200

0.2

0.4

0.6

0.8

1

1.2

Time (h)

Co

st

(€)

House 1

House 2

House 3


106

6.2.1.4 Scenario IV - Parameterization for comfort benefits

The fourth scenario is focused in maintaining the indoor comfort, all agents want to respect the

established temperature gap regardless the required consumption. To accomplish this goal, the

temperature penalty was significantly increased, and the consumption parameters decreased,

Table 6.5.

Table 6.5. Scenario IV - Penalty values

Parameter A1 A2 A3

𝛯 50000 50000 50000

1 1 3

ϕ 0.2 0.2 0.2

0.1 0.1 0.1

Figure 6.32. Scenario IV - Disturbance forecasting and indoor temperature A1.

0 5 10 15 200

0.5

1

1.5

2

Pow

er

(kW

)

0 5 10 15 2018

19

20

21

22

23

Time (h)

Tem

pera

ture

(ºC

)




107

Figure 6.33. Scenario IV - Disturbance forecasting and indoor temperature A2

Figure 6.34. Scenario IV - Disturbance forecasting and indoor temperature A3

Figure 6.35. Scenario IV – A1 power profile.

0 5 10 15 200

0.5

1

1.5

2

Pow

er

(kW

)

0 5 10 15 2021

21.5

22

22.5

23

23.5

24

Time (h)

Tem

pera

ture

(ºC

)

Temp. Max (ºC) Temp. Min (ºC) Indoor Temp. (ºC)


0 5 10 15 200

0.5

1

1.5

2

2.5

3

Pow

er

(kW

)

0 5 10 15 2020

21

22

23

24

25

Time (h)

Tem

pera

ture

(ºC

)



0 5 10 15 20-3

-2

-1

0

1

2

3

Pow

er

(kW

)

0 5 10 15 200

0.5

1

1.5

2

2.5

Time (h)

Pow

er

(kW

)




108

Figure 6.36. Scenario IV - A2 power profile.

Figure 6.37. Scenario IV - A3 power profile.

Figure 6.38. Scenario IV - Global consumption characterization.

0 5 10 15 20

-3

-2

-1

0

1

2

3

Pow

er

(kW

)

0 5 10 15 200

0.5

1

1.5

2

2.5

3

3.5

Time (h)

Pow

er

(kW

)



0 5 10 15 20-2

-1

0

1

2

Pow

er

(kW

)

0 5 10 15 200

0.5

1

1.5

2

Time (h)

Pow

er

(kW

)



0 5 10 15 200

0.5

1

1.5

2

2.5

3

3.5

4

Time (h)

Pow

er

(kW

)


Total Red (kW)

Total Green (kW)


109

As can be seen in Figure 6.32, Figure 6.33 and Figure 6.34 in all the indoor temperatures are

mostly maintained inside the comfort gap.

As consequence, the power constraints, Figure 6.35, Figure 6.36 and Figure 6.37, are violated

and the red resource consumption increased significantly,

Figure 6.38.

Figure 6.39. Scenario IV - Power profile.

Figure 6.40. Scenario IV - Heating/cooling total cost.

Being now the comfort a priority it’s quite clear that the controller tries to accomplished the pre-

defined comfort range leading to a consumption and cost surplus.

As expected, distinct results were obtained in the several proposed scenarios. Figure 6.41

summarize the obtained costs results for the 24hours simulation.

0 5 10 15 200

2

4

6

8

10

12

14

16

18

20

Time (h)

Po

we

r (k

W)

House 1 (kW)

House 2 (kW)

House 3 (kW)

0 5 10 15 200

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Time (h)

Cost

(€)

House 1

House 2

House 3


110

Figure 6.41. Daily heating/cooling total cost.

Comparing the economic differences between scenarios, the third scenario has shown to be the

most economical; the parameters penalizing the consumption were significantly increased,

leading to a situation of less energy usage. However, this decreased consumption led to a higher

indoor temperature deviation from the established boundaries. On the other hand, Scenario IV

was the most expensive. In this scenario the penalty value in the temperature constraint was

increased, showing that the consumers were only concerned in maintaining the temperature

inside the boundaries. Thus, all the necessary resources were consumed, leading to higher costs,

in order to respect the comfort limits. The possibility of obtaining comfort in detriment of the

cost may be important in various situations. For example: To acclimatize rooms with children or

areas in laboratories and/or hospitals. Remark that, despite this comfort preference, the cost

function (in due proportion given by the parameters) also minimizes all the other terms.

The parameterizations from the first and second scenarios have shown to be the most balanced,

with a compromise between comfort and costs.

6.3 Access order with variable hourly sequence

In this chapter it is considered that the sequence access order may vary hourly (Barata et al.,

2013a). The TCA bids are made according to the consumption needs. Each TCA is isolated (no

thermal interactions are considered), has a known fixed 24 hours consumption profile and it is

established a priority level from 1 (low) to 3 (high), that indicates how important that hour is in

terms of consumption. Thus, the hours with high priority levels indicates high consumption and

consequently a higher bid value, Table 6.7.

1 2 3

0.8

1

1.2

1.4

1.6

1.8

2

TCA's

€

Scenario I

Scenario 2

Scenario 3

Scenario 4


111

6.3.1 Algorithm II - Implemented sequential scheme with variable

hourly sequence

As mentioned it is considered that the sequence order was already stablished by a previous

auction, but in this chapter, the access sequence order vary hourly. The hourly access sequence

is storage in AO(NS×HP) as exemplified in Table 6.6 for NS=5 and HP=24. Each agent predicts

the consumption and subtracted it to maximum available communicates that information to the

next on the sequence list. Remark that, only the divisions that thermally interact pass to each

other the information about future indoor temperatures.

Table 6.6. Example of hourly access order sequence to green energy

Access

order

Time (h)

1 2 3 4 … 23 24

TCA 1 TCA 3 TCA 5 TCA 1 … TCA 4 TCA 1






112

Algorithm II - DSM-DMPC Implemented sequential scheme with variable hourly sequence

Required for all TCA’s: Thermal disturbances, comfort temperature gap, hourly constraints

parameters and hourly auction bid.

For all TCA’s Wi initialize:

𝐶𝑤𝑙𝑖 fixed consumption within HP (1 × 𝐻𝑃)

BV bid value by hour inside the HP (1 × 𝐻𝑃)

AO access order to green resource is established within the HP (𝑁𝑆 × 𝐻𝑃).

for k=1 to NC


Get the access order at current instant, AO(k)

Apply to all TCA 𝑢𝑙𝑖(𝑘 − 1: 𝑘 − 1 + 𝐻𝑃)from k-1 instant to obtain 𝑇𝑙

𝑖(𝑘: 𝑘 + 𝐻𝑃)



��𝑖(𝑘: 𝑘 + 𝐻𝑃) = ��𝑖(𝑘: 𝑘 + 𝐻𝑃) −∑𝐶𝑤𝑙𝑖(𝑘: 𝑘 + 𝐻𝑃)

𝑁𝑑𝑖

𝑙=1

Calculate the optimal control sequence 𝑢𝑙𝑖(1:𝐻𝑃) solving OPi (5.1)-(5.11) with power

constraints given by 𝑈𝑖 and ��𝑖



𝑁𝑑𝑖

𝑙=1

end for

Update batteries available energy

end for

Remark: generically, 𝑋(𝑘: 𝑘 + 𝐻𝑃) represents a line vector (1 × 𝐻𝑃) containing values from

𝑥(𝑘) to 𝑥(𝑘 + 𝐻𝑃), and 𝑌(𝑝, 𝑘: 𝑘 + 𝐻𝑃), represents the line p of a matrix (𝑃 × 𝐻𝑃) containing

values from y(𝑝, 𝑘) to y(𝑝, 𝑘 + 𝐻𝑃).

6.3.2 Results

Figure 6.42 presents the outdoor temperature and Figure 6.43 to Figure 6.45, presents the

known fixed 24 hours consumption profile and priority level from the three TCA’s.


113

Figure 6.42. Outdoor temperature forecasting (Toa).

Figure 6.43. Fixed consumption profile 𝐶𝑤11, and priority level of TCA1.


0 5 10 15 2015

20

25

30

35

40

Time (h)

Te

mp

era

ture

(ºC

)

Temp. Outside

0 5 10 15 200

1

2

3

4

Pow

er

(kW

)

0 5 10 15 201

1.5

2

2.5

3

Time (h)

Level

Fixed consumption A1(kW)

Priority Level

0 5 10 15 200

1

2

3

4

Pow

er

(kW

)

0 5 10 15 201

1.5

2

2.5

3

Time (h)

Level


Priority Level


114


As mentioned, the priority level presented is stablished according the consumption needs. Thus,

higher consumption represents higher priority levels, and consequently higher bid values, as

presented in Table 6.7.

Table 6.7. Bid value for each consumption level by agent.

Consumption Priority Level House 1 House 2 House 3

0-1 kW 1 2/50.09 3/50.09 1/20.09

1-2 kW 2 7/100.09 4/50.09 2/30.09

>2 kW 3 8.5/100.09 9/100.09 3/40.09

The bid value establishes an order to access to the resource, being the green resource

consumption made by the agents sequentially by that order. The first agent consumes and the

remainder green resource is passed to the next agent as the maximum green available resource.

As mentioned, when the green resource becomes insufficient to satisfy all the demand, the red

is available. The red resource consumption implies a penalty in the final cost function (5.1) due

to the soft constraint violation imposed by the maximum available green resource is exceeded.

A scheme of the system implemented is shown in the next picture.

Available green power

-

TgreenU

1U1

11 uU ….

-

1

1Cw2

1Cw

2

12 uU 2U

Figure 6.46. Implemented system.

0 5 10 15 200

1

2

3

4

5

Pow

er

(kW

)

0 5 10 15 201

1.5

2

2.5

3

Time (h)

Level

Priority Level



115

𝐶𝑤𝑙𝑖 = [𝑐𝑤𝑙

𝑖(𝑘), … , 𝑐𝑤𝑙𝑖(𝑘 + 𝐻𝑃)]

𝑇 (6.1)

𝑈𝑇𝑔𝑟𝑒𝑒𝑛 = [|𝑢𝑇𝑔𝑟𝑒𝑒𝑛(𝑘)|, … , |𝑢𝑇𝑔𝑟𝑒𝑒𝑛(𝑘 + 𝐻𝑃)|]𝑇 (6.2)

𝑢𝑙𝑖 = [|𝑢𝑙

𝑖(𝑘)|, … , |𝑢𝑙𝑖(𝑘 + 𝐻𝑃)|]

𝑇 (6.3)

where, for a generic TCA i at the control horizon, ��𝑖 represents the green available resource for

indoor comfort , UTgreen represents the green available total resource, 𝐶𝑤𝑙𝑖 the fixed consumption

profile from TCA i division l and 𝑢𝑙𝑖 the used power to heating/cooling the division l inside

TCA i, that results from the optimization program.

It is considered that all houses have the same outdoor temperature presented in Figure 6.42. The

thermal characteristics, load disturbances profile and comfort temperature bounds are different

for all houses. Agents can also have distinct penalties on power and temperature constraints

violations, they can hourly privilege comfort or cost according to consumer choice. Here, is

assumed that the penalty values of each agent are always the same. Table 6.8, shows the used

parameters.

Table 6.8. Scenario parameters.


Req 50 25 75 ºC/kW

Ceq 9.2103 4.6103 11103 kJ/ºC

𝛯 100 100 300 -

500 200 300 -

ϕ 2 2 2 -

1 1 1 -

t 1 1 1 h

HP 24 24 24 -

T(0) 24 23 24 ºC

As a result from the hourly variation of the priority levels, the bid values also vary hourly

yielding distinguish access orders as showed in Figure 6.47.


116

Figure 6.47. Access order.

Figure 6.48. Disturbance forecasting and indoor temperature A1.


0 5 10 15 201

2

3

Time (h)

Ord

er

A1 A3 A2

0 5 10 15 200

0.5

1

1.5

Time (h)

Pow

er

(kW

)


0 5 10 15 2020

22

24

26

Time (h)

Tem

pera

ture

(ºC

)

Indoor Temp.

Temp. Min.

Temp. Max.

0 5 10 15 200

0.5

1

Pow

er

(kW

)


0 5 10 15 2020

22

24

26

Time (h)

Tem

pera

ture

(ºC

)

Indoor Temp. Temp. Min. Temp. Max.


117


The thermal disturbances forecasts and the indoor temperature with its constraints for the TCA,

A1, A2 and A3 have the profile presented in, Figure 6.48, Figure 6.49 and Figure 6.50

respectively, and despite it and the access order variability, it can be seen in that the indoor

temperatures are always inside their narrow bounds. Taking advantage of the predictive

knowledge of the disturbance and making use of the space thermal storage, it can also be seen

that the MPC treats the indoor temperature before the disturbance beginning.

The Figure 6.51, Figure 6.52 and Figure 6.53 show for TCA, A1, A2 and A3 respectively, the

used power to acclimatize the spaces and the available green resource to do it. Remark that to

the green resource value must be subtracted the fixed consumption and then, the remainder

represents the maximum available power to provide comfort. Thus, in these figures the “Power

Max” represents the power constraint, ��𝑖 = ��𝑖−1 − 𝑢𝑖−1𝑙 − 𝐶𝑤𝑙

𝑖, “Green resource” ��𝑖−1 −

𝑢𝑖−1𝑙 , and ”Consumption” represents 𝑢𝑖

𝑙.

Figure 6.51. Consumption and constraints to heat/cool A1.

0 5 10 15 200

0.1

0.2

0.3

0.4

0.5

Pow

er

(kW

)


0 5 10 15 2020

22

24

26

Time (h)

Tem

pera

ture

(ºC

)

Temp. Min. Temp. Max. Indoor Temp.

0 5 10 15 20-2

-1

0

1

2

3

4

5

Time (h)

Pow

er (

kW)

Green resource (kW) Power Max (kW) Power Min (kW) Consumption (kW)


118



Figure 6.54. Global consumption.

In Figure 6.51 to Figure 6.53, it can be seen that the comfort constraints are respected, the used

power to heat/cool the space is maintained inside the constrained bounds. Note that when the

0 5 10 15 20-4

-3

-2

-1

0

1

2

3

4

5

Time (h)

Po

wer

(k

W)

Power Min (kW) Power Max (kW) Consumptiom (kW) Green resource (kW)

0 5 10 15 20-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

Time (h)

Po

wer

(k

W)

PowerMax (kW) Green resource (kW) Consumptiom (kW) Power Min (kW)

0 5 10 15 200

1

2

3

4

5

6

7

8

Time (h)

Pow

er

(kW

)

Red Resouce (kW) Green Resource (kW) Total Available (kW)


119

resource is null the consumption is also null. Figure 6.54 shows the global used power and

characterized it in terms of type of consumed power.

𝑈𝑢𝑠𝑒𝑑(𝑘) =∑[|𝑢𝑙𝑖(𝑘)| + 𝐶𝑤𝑙

𝑖].

It can be seen in Figure 6.54, that in the most demanding periods, the maximum green available

resource is exceeded and the red resource must be consumed.

Figure 6.55. Heating/cooling total cost.

Figure 6.55 illustrates the effectiveness of the approach and demonstrates the advantage of the

auction. For each one of the agents it can be seen that the “Real Cost” is much lower than the

cost of not to bid in auction and only consume the red resource “Red Cost”.

6.4 Conclusions

In this chapter, a distributed MPC control technique was presented in order to provide thermal

house comfort. The solution obtained solves the problem of controlling multiple subsystems

dynamically coupled and also exposed to a coupled constraint. Each subsystem solves its own

problem by involving its own state predictions or from neighbourhoods and the shared

constraints. It could be observed through the simulations and result’s analysis that suitable

dynamic performances were obtained. The built system is flexible in two ways. It allows in each

auction the agents to bid higher or lower in accordance with their needs and, by changing the

penalty values during the day, consumers can shift hourly between indoor comfort and lower

costs. Knowing in advance the disturbance forecasts allows agents to make their bid and

achieve significant savings at the end of the day.

The distributed MPC control technique, along with a thermal-electrical modular scheme, was

validated in order to provide thermal house comfort, with strong presence of intermittent/limited

0 5 10 15 200

0.2

0.4

0.6

0.8

1

1.2

1.4

Time (h)

Cost

(€)

Red Cost A1

Red Cost A2

Red Cost A3

Real Cost A1

Real cost A2

Real Cost A3


120

RES environments. The approach spots a control problem of multiple subsystems dynamically

coupled and exposed to coupled constraint. Each subsystem solves its own problem by

involving its own state predictions and the state predictions of adjacent rooms, available with

communication interchange and shared constraints. The changing in penalty values allows

consumer to pick between indoor comfort and lower costs.

121

Chapter 7

7 DMPC for Thermal House Comfort

with Sliding Load

7.1 Introduction

The desired approach here presented intends to take advantage from the innovative technology

characteristics provided by future SGs (Korolija et al., 2011). In the smart world, simple

household appliances, like dishwashers, clothes dryers, heaters or air conditioners are assumed

to be fully controllable in order to achieve the network maximum efficiency. Renewable

energies will be a common presence and any kWh provided by these technologies should not be

wasted. Active Demand-Side Management will control the loads in order to adapt them to the

available renewable energy source. As mentioned in Chapter 2.2, DSM studies are focused in

the development of load control manipulation models (EIA, 2014; Favre-Perrod et al., 2009)

and electricity incentive prices to promote load management (Kosek et al., 2013; Chen, 2010).

In buildings, DSM is based on an effective reduction of the energy needs by changing the shape

and amplitude consumer’s load diagrams. So, DSM can involve a combination of several

strategies; pricing, load management curves and energy conservation are implemented for a

more energy efficient use.

Load shifting is considered a common practice in the management of electricity supply and

demand, where the peak energy use is shifted to less busy periods. Properly done, load shifting

helps meeting the goals of improving energy efficiency and reducing emissions, smoothing the

daily peaks and valleys of energy use and optimising existing generation assets. With new

technological advances, DR programmes may shift loads by controlling the function of air

CONTROL FOR THERMAL HOUSE COMFORT WITH SLIDING LOAD

122

conditioners, refrigerators, water heaters, heat pumps and other similar electric loads at

maximum demand times. The work here presented is distinct because provides an integrative

solution which is able to, in a distributed network with multiple TCAs, adjust the demand to an

intermittent limited energy source, using load shift and maintaining the indoor comfort, (Barata

et al., 2013c) and more detailed in (Barata et al., 2014c). Figure 7.1, exemplifies a shifting load

communication infrastructure.

Figure 7.1. Shifting load communication infrastructure.

Thus, due the specificities made in this chapter, the following assumptions are added to the ones

made in Chapter 6.1:

Each division selects the load value (LV), the duration (LVd), the turned on time (ToT)

and the “sliding level” (SL) of the “shifted loads”. The SL indicates that the load can

be turned on SL hours before and after the chosen ToT;

The next picture illustrates the shifting load characteristics.

Figure 7.2. Implemented shifting load scheme.

Therefore, using the demand side management, by negotiating the energy price and the

consumer comfort, the distributed loads can be managed and shifted in order to guarantee the

Shifting load

Controler

Shiftable loadsHVAC, Dishwaher, PHEV,…

Non-Shiftable loadsLigthing, Frigde ,…

Communication Line

Power Line

Consumer

Parameterization

ToT

LVd

LV

SL=1 SL=1SL=2 SL=2

1

...

2

...

LV

...

Po

wer

(k

W)

Time (h)


123

satisfaction of all constraints. The global system includes an auction (provided by the MO) that,

in accordance with the bid value made by the houses/agents, defines an order to access the

green resource. The green resource consumption is made by the agents sequentially by the

auction order and the information about the remaining green resource is passed to the next agent

as the maximum green available resource. As mentioned, when green resource becomes

insufficient to satisfy all the demand, the red is available.

7.2 Algorithm III – Implemented shifting and loads allocation

scheme

Each one of the systems starts by choosing their loads characteristics, LV, LVd, ToT and SL. With

this data, all the possible loads schedule combinations (PLSCS) are establish (see Figure 7.7

e.g.). At each time step, it’s verified if inside the predictive horizon, any PLSCS exceeds the

maximum available green energy iU max . The sequences that are at any instant above the

iU max limit are removed, and the remaining are the feasible load schedule combinations

(FLSCS). The FLSCS are subtracted to iLU , and the resulting in a set of combinations iU that

are tested in the minimization problem as maximum available green resource for comfort (5.1).

The hypothesis that provided less consumption is chosen. Once one sequence is started, all the

others that are different until the current step time are eliminated until the final load sequence is

chosen, FLSeq. The total consumption by division and house at any instant can be written as

(7.1) and (7.2) respectively, and is pictured in Figure 7.4.

Figure 7.3. Total consumption characterization.

Remark that the total available for comfort for each house (7.3) is used as constraint in the

optimization problem. The equations assume the following form,

𝑃𝑙𝑖(𝑘) = |𝑢𝑙

𝑖(𝑘)| + 𝐶𝑤𝑙𝑖(𝑘) + 𝐹𝐿𝑆𝑒𝑞𝑙

𝑖(𝑘), (7.1)

𝑃𝑖(𝑘) =∑𝑃𝑙𝑖(𝑘)

𝑁𝑑𝑖

𝑙=1

, (7.2)


124

𝑈𝑖(𝑘) = 𝑢 𝑇𝑔𝑟𝑒𝑒𝑛(𝑘) −∑(𝐶𝑤𝑙𝑖(𝑘) − 𝐹𝐿𝑆𝑒𝑞𝑙

𝑖(𝑘))

𝑁𝑑𝑖

𝑙=1

−∑𝑃𝑗(𝑘)

𝑁𝑆

𝑗=1𝑖≠𝑗

. (7.3)

A simplified scheme of the implemented optimization problem is shown in the next picture,

Figure 7.4, followed by the implemented DSM-DMPC algorithm.

TgreenUU 1max

--

iU

OPi

iLU

iTgreeni PUU 1max

--

--

OPNS

1

1

maxS

S

N

i

iTgreenN PUU

Wi

SNW

iPSLC

iNd

l

i

lCw

1iU

1iLU

12max iiTgreeni PPUU

Wi+1

1iPSLC

1

1iNd

l

i

lCw

OPi+1

SNU

SNLU1iPSLC

SN

S

Nd

l

N

lCw

Figure 7.4. Implemented power distribution scheme starting in the Optimization Problem 1

(OPi) to OPNS.


125

Algorithm III - DSM-DMPC pseudocode prototype algorithm

For all houses Wi initialize:

LV load value

LVd the duration

ToT the turned on time

SL sliding level

iPSLC possible schedule loads combinations (𝑛𝑃𝐶 ×𝐻𝑃) with nPC the number of possible

combinations

𝐶𝑤𝑙𝑖 fixed consumption within HP (1 × 𝐻𝑃)

BV bid value by hour inside the HP (1 × 𝐻𝑃)

AO access order to green resource is established within the HP (𝑁𝑆 × 𝐻𝑃).

for k=1 to NC


Get the access order at current instant, AO(k)

Apply to all TCA 𝑢𝑙𝑖(𝑘 − 1: 𝑘 − 1 + 𝐻𝑃)from k-1 instant to obtain 𝑇𝑙

𝑖(𝑘: 𝑘 + 𝐻𝑃)



��𝐿𝑖(𝑘: 𝑘 + 𝐻𝑃) ← ��𝑚𝑎𝑥𝑖(𝑘: 𝑘 + 𝐻𝑃) −∑𝐶𝑤𝑙𝑖(𝑘: 𝑘 + 𝐻𝑃)

𝑁𝑑𝑖

𝑙=1

Built table with all FSLCS

𝐹𝐿𝑆𝐶𝑖(𝑛𝐹𝐶 , 𝑘: 𝑘 + 𝐻𝑃) ← 𝑃𝐿𝑆𝐶𝑖(𝑛𝐹𝐶 , 𝑘: 𝑘 + 𝐻𝑃) − ��𝐿𝑖(𝑘: 𝑘 + 𝐻𝑃) ≥ 0

for t=1 to nFC (number of feasible combinations)

Calculate the optimal control sequence ui(1:HP) solving OPi (5.1)-(5.11) with power

constraint given by ��𝑖(𝑘: 𝑘 + 𝐻𝑃) ← 𝐹𝐿𝑆𝐶𝑖(𝑡, 𝑘: 𝑘 + 𝐻𝑃)

𝑈𝑝𝑟𝑒𝑑𝑖(𝑡) ← ∑𝑢𝑖(1:𝐻𝑃)

if 𝑈𝑝𝑟𝑒𝑑𝑖(𝑡) < 𝑈𝑝𝑟𝑒𝑑𝑖(𝑡 − 1) then

𝐹𝐿𝑆𝑒𝑞𝑖(1: 𝑘) ← 𝐹𝑆𝐿𝐶𝑖(𝑡, 𝑘: 𝑘 + 𝐻𝑃)

end if

end for

Eliminate from 𝑃𝐿𝑆𝐶𝑖 all the sequences that are different from 𝐹𝐿𝑆𝑒𝑞𝑖(1: 𝑘)



𝑁𝑑𝑖

𝑙=1

end for

Update batteries available energy

end for


126

As mentioned the algorithm is sequential, and for a better understanding of the implemented

power distribution scheme, the access order is W1, W2 and so on. Therefore, for a certain instant,

is considered that W1 was the one that made the highest bid, W2 made the second highest, always

sequentially until 𝑊𝑁𝑆 . In Figure 7.4, the available power for W1 is given by the predicted green

total available resource 𝑈𝑚𝑎𝑥1 = 𝑈𝑇𝑔𝑟𝑒𝑒𝑛 at the control horizon (7.5), and them the fixed

consumption (7.4) is subtracted resulting in 𝑈𝐿𝑖. As mentioned, the PLSCS are compared inside

the predictive horizon with 𝑈𝐿𝑖, and the ones that exceeds at any instant limit are removed,

and the remaining are FLSCS. The FLSCS are subtracted to , and the resulting in a set of

combinations 𝑈𝑖.. These combinations are the power constraint (5.10) and are tested in the OPi

(5.1). The combination that generate lower consumption, ui , is chosen. Then, the information

about the available green energy is passed for the next house, 𝑈𝑚𝑎𝑥𝑖.

For a generic Agent i at the control horizon 𝑈𝑇𝑔𝑟𝑒𝑒𝑛 represent the green available total resource,

𝐶𝑤𝑙𝑖 the fixed consumption profile and 𝑢𝑙

𝑖the used power to heating/cooling the space that

results from the optimization program. These parameters are express by the vectors (7.4)-(7.6),

𝐶𝑤𝑙𝑖 = [𝑐𝑤𝑙

𝑖(𝑘), . . . , 𝑐𝑤𝑙𝑖(𝑘 + 𝐻𝑃)]

𝑇, (7.4)

𝑈𝑇𝑔𝑟𝑒𝑒𝑛 = [|𝑢𝑇𝑔𝑟𝑒𝑒𝑛(𝑘)|, . . . , |𝑢𝑇𝑔𝑟𝑒𝑒𝑛(𝑘 + 𝐻𝑃)|]𝑇, (7.5)

𝑢𝑙𝑖 = [|𝑢𝑙

𝑖(𝑘)|, . . . , |𝑢𝑙𝑖(𝑘 + 𝐻𝑃)|]

𝑇. (7.6)

In the built algorithm it is considered that the access order to the green resource is established

hourly according to bid value made in auction by each agent, and therefore, at each instant the

defined access sequence must be applied. Another feature provided by the implemented system

is that each house can have different hourly penalties, allowing the consumer to choose between

more/less comfort and cost during the day.

7.3 Results

The presented results were obtained with an optimization MATLAB® routine that finds a

constrained minimum of a quadratic cost function that penalizes the sum of the several

objectives (5.1).


127

7.3.1 One house scenario

To simplify better understand the used approach, the first results here present show only the

shifting loads procedure for one house represented by one division with thermal disturbance

(QPd), Figure 7.6 (no fixed consumption profile and storage are considered). Table 7.1 shows the

used scenario parameters. The outdoor temperature forecast, Figure 7.5, considers 90%

accuracy to within +/- 2°C on the next day.

Figure 7.5.Outdoor temperature forecasting (Toa).

Table 7.1.Scenario parameters

Req(ºC/kW) Ceq(kJ/ºC) Ξ Ψ ϕ 𝜑 t(h) HP NC T(0) (ºC)

50 9.2103 500 500 2 1 1 24 24 21

Figure 7.6. Thermal disturbance forecasting.

2 4 6 8 10 12 14 16 18 20 22 2415

20

25

30

35

40

Time (h)

Te

mp

era

ture

(ºC

)

Outdoor Temp.

2 4 6 8 10 12 14 16 18 20 22 240

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Time (h)

Pow

er

(kW

)

Disturbance thermal load (kW)


128

The Loads that can be daily shifted have the characteristics present in the next Table 7.2, and

Figure 7.7 shows all the possible 56 loads combinations in the 24hours period.

Table 7.2. Shifted loads characteristics

Loads LV (kW) LVd (h) ToT (h) SL (h)

Load 1 3 2 8 3

Load 2 2 3 18 4

Figure 7.7. Possible loads schedule combinations (PLSCs).

The system tests all combinations present in Figure 7.7, and as mentioned above, the hypotheses

that do not respect the maximum predicted green resource are initially discharge, and the

remaining ones the FLSCS, Table 7.3, are tested in (5.1).

The sequence FLSeq, where mostly green energy is consumed, the costs are lower and the

indoor comfort range is respected is found.

510

1520

10

20

30

40

50

0

1

2

3

Time (h)

PLSCS

Pow

er

(kW

)


129

Table 7.3. Feasible Loads Sequence Combinations

FL

SC

Time (h)

1 2 3 4 5 6 7 8 9 10 11 12

1 0 0 0 0 0 0 0 0 3 3 3 0

2 0 0 0 0 0 0 0 0 3 3 3 0

3 0 0 0 0 0 0 0 0 3 3 3 0

4 0 0 0 0 0 0 0 0 3 3 3 0

FL

SC

Time (h)

13 14 15 16 17 18 19 20 21 22 23 24

1 0 2 2 2 2 0 0 0 0 0 0 0

2 0 0 2 2 2 2 0 0 0 0 0 0

3 0 0 0 2 2 2 2 0 0 0 0 0

4 0 0 0 0 2 2 2 2 0 0 0 0

In Figure 7.8 are the total energy costs of the FLSCS shown in Table 7.3, and can be seen that

the chosen sequence is the less expensive.

Figure 7.8. Total energy costs of FLSCS.

Figure 7.9, show the chosen load sequence, FLSeq, and the available green energy to allocate

the loads.

1 2 3 40.265

0.266

0.267

0.268

0.269

0.27

0.271

0.272

0.273

0.274

Hypothesis

€

Total Cost Hypothesis (€)


130

Figure 7.9. Maximum available green energy and chosen sequence.

In order to minimize the energy costs by consuming only green resource, the implemented

algorithm chooses the gaps that fit properly in the maximum available green energy.

Figure 7.10. Indoor temperature.

The comfort limits varies during the 24h period, and Figure 7.10 shows that the indoor

temperature is always maintained inside the comfort limits being the optimization problem able

to respect the temperature and power constraint Figure 7.11.

The periods between 9-11h and 15-18h are extremely demanding, all green energy is consumed

by the shifted loads, with no remaining one for comfort proposes.

Although, Figure 7.10 shows that in that periods the algorithm choose to not use the red

resource and, taking advantage of the prediction horizon, pre-heat or pre-cool the spaces when

only renewable resource is available.

2 4 6 8 10 12 14 16 18 20 22 240

0.5

1

1.5

2

2.5

3

Time (h)

Pow

er

(kW

)

Initial Power Max.

Load Sequence

2 4 6 8 10 12 14 16 18 20 22 2421

21.5

22

22.5

23

23.5

24

Time (h)

Tem

pera

ture

(ºC

)

Indoor Temp.

Temp. Max.

Temp. Min.


131

Figure 7.11. Used power to heat/cool the space and the maximum green resource available for

comfort.

7.3.2 Distributed scenario

It is considered that all houses are represented by one division and have the same outdoor

temperature presented in Figure 7.5. The used parameters are presented in Table 7.4.

Table 7.4. Distributed scenario parameters


Req 50 25 75 ºC/kW

Ceq 9.2103 4.6103 11103 kJ/ºC

𝛯 100 100 300 -

𝝍 500 200 300 -

𝝓 2 2 2 -

𝝋 1 1 1 -

t 1 1 1 h

HP 24 24 24 -

T(0) 21 23 24 ºC

2 4 6 8 10 12 14 16 18 20 22 24-3

-2

-1

0

1

2

3

Time (h)

Pow

er

(kW

)



132

The batteries capacity is 3kWh. To incentive the clean resource consumption, it is considered

that the green energy price per kWh has a maximum auction value (0.09€/kWh) always cheaper

than the red energy price (0.17€/kWh). Table 7.5 shows the bid value for each one of the

priority levels that, as mentioned, are established according the fixed consumption profile.

Table 7.5. Bid value for each consumption level by TCA

Consumption Priority Level TCA 1 TCA 2 TCA 3

0-1 kW 1 2/50.09 3/50.09 1/20.09

1-2 kW 2 7/100.09 4/50.09 2/30.09

>2 kW 3 8.5/100.09 9/100.09 3/40.09

The load disturbances profile, comfort temperature bounds and shifted loads characteristics are

different for all houses, Table 7.6.

Table 7.6. Shifted loads characteristics for distributed scenario

TCA Loads LV (kW) LVd (h) ToT (h) SL (h)

1 Load 1 1 2 7 1

Load 2 2 4 18 2

2 Load 1 2 3 9 1

Load 2 2 2 21 2

3 Load 1 3 3 8 1

Load 2 3 3 13 1

In all houses, the fixed consumption profile, 𝐶𝑤11, 𝐶𝑤1

2 and 𝐶𝑤13 and its priority level, are

known within a 24h period and are depicted in Figure 7.12, Figure 7.13 and Figure 7.14.


1 3 5 7 9 11 13 15 17 19 21 23 240

0.5

1

1.5

2

2.5

3

Pow

er (

kW)

1 3 5 7 9 11 13 15 17 19 21 23 241

1.5

2

2.5

3

Time (h)

Leve

l


Priority Level


133



Figure 7.15. Access order.

1 3 5 7 9 11 13 15 17 19 21 23 240

1

2

3

4

Pow

er

(kW

)

1 3 5 7 9 11 13 15 17 19 21 23 241

1.5

2

2.5

3

Time (h)

Leve

l

Priority Level


1 3 5 7 9 11 13 15 17 19 21 23 240

1

2

3

4

Pow

er

(kW

)


0 5 10 15 201

1.5

2

2.5

3

Time (h)

Leve

l

Priority Level

2 4 6 8 10 12 14 16 18 20 22 241

2

3

Time (h)

Ord

er

A3 A2 A1


134

As a result from the hourly variation of the priority levels, the bid values also vary hourly

yielding distinguish access orders as showed in Figure 7.15.

The thermal disturbance profile is known within a 24 hour period, and is related with thermal

loads generated by occupants, direct sunlight, electrical devices or doors and windows aperture

to recycle the indoor air.



1 3 5 7 9 11 13 15 17 19 21 23 240

0.2

0.4

0.6

0.8

1

Pow

er

(kW

)

1 3 5 7 9 11 13 15 17 19 21 23 2418

20

22

24

26

Tem

pera

ture

(ºC

)

Time (h)

Indoor Temp. Temp. Max. Temp. Min.


1 3 5 7 9 11 13 15 17 19 21 23 240

0.2

0.4

0.6

0.8

1

Pow

er

(kW

)

Time (h)


1 3 5 7 9 11 13 15 17 19 21 23 2420

21

22

23

24

25

26

Tem

pera

ture

(ºC

)

Temp. Max. Temp. Min. Indoor Temp.


135


In Figure 7.16, Figure 7.17 and Figure 7.18, it can be seen that the comfort constraints are

respected, the indoor temperature is always inside the comfort zone in all houses. Taking

advantage of the predictive knowledge of the thermal disturbance and making use of the space

thermal storage, it can also be seen that in all houses the MPC treats the indoor temperature

before the thermal disturbance beginning. In Figure 7.19 it can be seen that the shifted loads

were located in zones with mostly green energy available. Note that when the used power is

above the daily maximum green available resource, means that the red resource was consumed.

The used power to heat/cool the space is maintained inside the constrained bounds and when the

green energy is null the used power is also null, Figure 7.20, Figure 7.22 and Figure 7.24 for

TCA1, TCA2 and TCA3 respectively.

Remark that the fixed consumption, 𝐶𝑤11, 𝐶𝑤1

2 and 𝐶𝑤13 represent the base in the power profile

in Figure 7.19, Figure 7.21 and Figure 7.23.

Figure 7.19. Power profile A1.

0 5 10 15 200

0.1

0.2

0.3

0.4

0.5

Pow

er

(kW

)


0 5 10 15 2021

22

23

24

25

26

Time (h)

Tem

pera

ture

(ºC

)

Temp. Max. Temp. Min. Indoor Temp.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 240

1

2

3

4

5

6

7

8

9

10

Time (h)

Pow

er

(kW

)

A1

Red consumption (kW)

Control Input (kW)

Load Sequence (kW)

Fixed consumption forecast (kW)

Power Constraint (Max Available) (kW)


136

Remark that, for example, at time instant t=7, three different types of energy utilization are

used. The base, in dark grey, is fulfil with the fixed consumption, above is the shifted load and

on top is the used power for comfort. In this instant the total consumption is maintained within

the power constraint. On the other hand, at instant t=9, with no available green power, all the

fixed consumption of 2kW is made with red resource.

Figure 7.20. Control input profile A1

In Figure 7.21, it can be seen that the shifted loads of house 2 were located in zones with mostly

green energy available.


The used power to heat/cool the space is always maintained inside the constrained bounds been

the clean resource consumed only when is available. Note that when the used power to satisfy

all the demand is above the daily maximum green available resource, means that the red

resource was consumed, Figure 7.21.

1 3 5 7 9 11 13 15 17 19 21 23 24-8

-6

-4

-2

0

2

4

6

8

Time (h)

Pow

er

(kW

)

Power Min (kW) Power Max (kW) Consumption (kW)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 240

1

2

3

4

5

6

7

8

9

Time (h)

Po

we

r (k

W)

A2


Control Input (kW)

Load Sequence




137

Figure 7.22. Control input profile A2.

Figure 7.23 shows that the chosen FLSeq3 is located here the consumption of red resource is

obliged. Due the access order imposed by the auction, the maximum available energy may

change hourly, and by this fact the available resource prediction is not as effective as with one

house only. Also, the SL=1 of both loads of house 3 Table 7.6, is obvious a conditionality and

an extra restriction on our optimization algorithm.

The power constrained bounds are respected been the consumed made only when the clean

resource is available, Figure 7.24.


2 4 6 8 10 12 14 16 18 20 22 24-8

-6

-4

-2

0

2

4

6

8

Time (h)

Pow

er

(kW

)


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 240

1

2

3

4

5

6

7

8

9

10

Time (h)

Pow

er

(kW

)

A3


Control Input (kW)

Load Sequence




138

Figure 7.24. Control input profile A3.

Figure 7.25. Batteries profile.

.

Figure 7.26. Consumption costs.

2 4 6 8 10 12 14 16 18 20 22 24

-6

-4

-2

0

2

4

6

Time (h)

Pow

er

(kW

)


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 240

0.5

1

1.5

2

2.5

3

Time (h)

Pow

er

(kW

)

Batteries Available Power

2 4 6 8 10 12 14 16 18 20 22 240

0.2

0.4

0.6

0.8

1

1.2

1.4

Time (h)

Co

st

(€)

Red Cost A3 Red Cost A1 Red Cost A2 Real Cost A1 Real Cost A3 Real cost A2


139

The batteries profile during the 24h period is show in Figure 7.25. It can be seen that in the most

demanding periods, the energy available in the batteries provide a useful energy support. Figure

7.26 demonstrates the advantage of the auction. For each one of the houses it can be seen that

the “Real Cost” is much lower than the cost of not to bid in auction and only consume the red

resource “Red Cost” at a higher fixed price.

7.4 Conclusions

In this chapter, a distributed MPC control integrative solution was validated in order to provide

thermal house comfort in an environment with strong presence of intermittent/limited RES. The

approach spots a control problem of multiple subsystems (multi-agent) subjected to coupled

constraint solved as a sequence of QP optimization problems for each instant in time.

The approach shows that distributed predictive control is able to provide house comfort within a

DSM policy, based in a price auction and the rescheduling of appliance loads. It is a valid

methodology to achieve reduction in consumption and price. The approach is more effective

with wider periods where the loads are allowed to slide and consequently allocate the most

favourable zone.


140

141

Chapter 8

8 Conclusions and Future Work

Directions

8.1 Conclusion and Summary of Achievements

It is widely accepted that in a nearby future Smart Grids will be a part of our daily life’s. Smart

grids will most likely include decentralized generation, active network generation management,

energy storage and demand management resources, where the actions of all agents connected to

the electricity system can be intelligently integrated aiming for a sustainable, efficient and

secure energy supply system. Widespread communications and control technologies required to

use DR help maintain the supply-demand balance in electricity systems. Smart household

appliances with controllable loads will soon be a common presence in our homes. This active

DSM is able to manage the loads to obtain harmony in demand supply ratio, they also include

load control manipulation models, pricing, with distinct electricity tariffs along the day,

encouraging load management and other approaches which promote energy efficiency and

conservation. Many energy consumers are already able to tie the electricity pricing into their

energy management system, resulting in greater shifts of energy usage. This needs to be

convoyed by the application of intelligent appliances that would facilitate the implementation of

DSM.

Therefore, this work intends to be a solution which is able to respond to all this requirements.

The work has considered environmental issues and pre-establishes variables as a decision-maker

factor. In particular, the work presented a novel multi-agent model-based predictive control

method to manage distributed energy resources (DER) systems from the demand side, when in

CONCLUSIONS AND FUTURE WORK DIRECTIONS

142

presence of limited energy sources with fluctuating output and with energy storage in house-

hold or car batteries. Specifically, the work has presented a solution for thermal comfort which

is able to manage a limited shared energy resource via a demand side management perspective,

using an integrated approach also involving a power price auction and an appliance load

allocation scheme. The control technique has shown to be capable of controlling loads based on

the available supply at a certain time, without significantly compromising the user satisfaction.

The developed building’s energy management system and smart thermostat feature a lot of

programmable settings that allow users and their utilities to maximize energy savings. It is

based on a consumer's schedule or peak time’s energy demand for the utility; and in a

thermostat that pre-programs itself based on weather forecasts to optimize both consumer's

energy savings and grid performance. The system uses, weather conditions forecasts and the

MPC features to anticipate major changes in weather and manages heating and cooling needs in

advance, in the most energy-efficient way.

The term Thermal Control Area (TCA) was presented and described as an entity that is

embedded in a distributed environment, where several others TCA’s are working individually to

achieve their own goal and sharing their information to accomplish a global objective.

An electro-thermal modular scheme was developed to allow an easy building’s modelling with

different plans where adjacent areas with distinct construction features may thermally interact.

The global scenario described in Chapter 5 present all the basic assumptions in which the work

was developed. Also in this chapter the DMPC optimization problem and the Algorithm I which

define the implemented basic sequential scheme, were detailed, formalized and exemplified.

The obtained results showed its suitability.

In Chapter 6 was presented a solution that solves the problem of control of multiple subsystems

dynamically coupled and also stringed to a coupled constraint. Each subsystem solves its own

problem by involving its own state predictions, or from neighbourhoods, and the shared

constraints. It can be observed throughout the simulations and results analysis that suitable

dynamic performances were obtained. The system built in Algorithm II is flexible in two ways.

It allows in each auction the agents bid higher or lower in accordance with their needs and, by

changing the penalty values during the day, the consumer is able to hourly shift between indoor

comfort and lower costs. By knowing in advance the disturbance forecasts, the TCA’s are able

to make their bid and achieve significant savings at the end of the day.

In Chapter 7, a distributed MPC control integrative solution has been validated in order to

provide thermal house comfort in an environment with strong presence of intermittent/limited

RES. The developed Algorithm III has shown that distributed predictive control combined with

a DSM policy is a tool able to provide thermal comfort, based in a price auction and the


143

rescheduling of appliance loads. It is a valid methodology to achieve less energy consumption

and price reductions. The approach has shown to be more effective with wider periods where

the loads are allowed to slide and consequently allocate the most favourable zone.

The followed table summarize the implemented features which characterises the developed

algorithms.

Table 8.1. Developed algorithm characteristics

Features Algorithm I Algorithm II Algorithm III

Access to green energy Fixed Variable (hourly) Variable (hourly)

Distributed nature Yes Yes Yes

Thermal coupling Yes Yes Yes

Information interchange

between TCA’s Yes Yes Yes

Thermal disturbances Yes Yes Yes

Hourly penalties

variability No Yes Yes

Battery storage No Yes Yes

Fixed load allocation No Yes Yes

Priority consumption

level No Yes Yes

Sliding load allocation No No Yes

8.2 Recommendations for Future Work Directions

In order to efficiently allocate resources to facilitate balancing of both electricity and heat it

would be critical to establish some form of RTP arrangement so users could be fully informed

about the value of heat and electricity at each point in time (and location). This would also

encourage development of appropriate demand side solutions. This will require introduction of

much more sophisticated energy metering (e.g. half hourly metering) and trading functions and

would lead to deployment of information and communication systems to ease control of

generators and loads. The philosophy of liberal markets assumes economic optimums can only

be achieved through negotiations in a free market environment. Because energy is a complex


144

commodity, a sophisticated commercial structure is necessary to make possible the trading

between each generator or consumer and purchasers of energy and adjuvant services.

A market with hundreds of thousands or even millions of active participants is clearly a major

challenge. All participants will need to access various markets to set up long and short term

energy transactions, secure access to the network and provide ancillary services to operate the

system in a satisfactory manner (if this is to be done in heat energy, heat networks which would

facilitate operation of markets for heat would be required). In order to smooth trading of energy

among a very large number of distributed generators and loads, an electronic energy market

system, supported by the internet, would be needed to be developed.

RES forecasts of long-term power variation should be considered for a future task. As a rational

assumption, it is presumed that RES forecasts are within a short error band, negligible for

predicting horizons of 24 hours, but should be estimated for the effect of power variation during

longer periods.

Typically, distributed RES fluctuations are counter-balanced by the use of battery storage

systems. However, battery systems not only increase the size and cost of RES power systems

but also power fluctuations have the effect of reducing the useful life-time of the battery storage

system. The use of the battery storage system can, therefore, be fully optimised, minimising

storage requirements, avoiding damage to the battery bank and reducing power fluctuations with

the consequent useful life of the battery extent . These issues are key topics for future work.

Grid losses were also not considered in this work, they depend on the specific conductors, the

current flowing and the length of the transmission line. However, this work has considered

distributed resources that, when compared with typical grid framework, reduce the required net

inflow from the grid, reduce grid current and hence the grid losses. Thus, in future works grid

losses should be considered. To account for actual grid capacities and losses, larger-scale

simulations based on the grid network models should be applied to enable an effective analysis

of grid stability.

Recent software applications like Google Now (Google Now, 2012) provides an mechanism

that is able to inference about the users habits and suggest what is best at the right time, the

technology proactively delivers to users information that it predicts (based on their search

habits) they may want. Thus, based on the consumer habits, a future approach should take in

consideration this type of tool, to advice, in real time the user about consumption measures that

can be taken in to account to increased efficiency and reduce energy costs.

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